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  • Kinematic and dynamic analysis of a novel parallel kinematic Schönflies motion generator
    Mech. Mach. Theory (IF 3.535) Pub Date : 2020-01-18
    Alaleh Arian; Mats Isaksson; Clément Gosselin

    This paper analyses the kinematics and dynamics of an over-constrained parallel mechanism with four degrees of freedom providing Schönflies motion with infinite tool rotation. Despite its limited motion capability in one translational degree of freedom, the proposed mechanism has several potential uses, such as assembly of electronic components or fabric cutting. Firstly, the instantaneous kinematic problem of the investigated mechanism is presented, which includes formulating the inverse kinematics for the position, velocity and acceleration of the mechanism. Then, singular configurations of the manipulator are studied, based on the obtained Jacobin matrices. Secondly, based on the foregoing kinematic relations and the concept of link Jacobian matrices, the dynamic model is formulated by means of the principle of virtual work. Finally, the correctness of the derived models is verified by comparing the results obtained from the formulated models with those obtained using MATLAB Simscape Multibody.

    更新日期:2020-01-21
  • On discontinuous dynamics of a class of friction-influenced oscillators with nonlinear damping under bilateral rigid constraints
    Mech. Mach. Theory (IF 3.535) Pub Date : 2020-01-15
    Chenjing Dou; Jinjun Fan; Chunliang Li; Jing Cao; Min Gao

    This article is concerned with the discontinuous dynamical behaviors of a class of single degree of freedom oscillators with linear and nonlinear springs and viscous dampers in the co-existence of bilateral rigid impact and friction through the theory of flow switchability and flow barrier in discontinuous dynamical systems, where considering the inequality of static and kinetic friction coefficients. By the analysis of vector fields and G-functions on the corresponding discontinuous boundaries for such an oscillator, the analytical conditions of all possible motions are established, which are in the form of a set of inequalities or equalities and can be used for the selection of control parameters in this kind of system. Additionally, based on mapping dynamics, the two-dimensional basic mappings are defined, the analytical predictions and stability analysis of different periodic motions are accomplished. Finally, our theoretical results are further demonstrated by numerical simulations by means of dimensional and dimensionless parameters with graphical illustrations of the time histories of displacement, velocity, G-function and the trajectories in phase space for the passable motion, stuck motion, impact motion, grazing motion and periodic motion etc., and stick and grazing bifurcation scenarios varying with excitation frequency and amplitude are also given.

    更新日期:2020-01-15
  • Reflecting on the life of Kenneth H. Hunt and his contributions to Mechanism
    Mech. Mach. Theory (IF 3.535) Pub Date : 2020-01-14
    Gordon R. Pennock

    Kenneth Henderson Hunt, see Fig. 1, was the Foundation Professor of Engineering, and the inaugural Dean of the Faculty of Engineering at Monash University, Victoria, Australia. He was the Dean of Engineering from 1961 until 1975 and then served as the Chair of Mechanism from 1976 until 1985. He is remembered as the scientist who rediscovered Ball's theory of screws and who made significant contributions to screw system theory which he applied to the kinematics of spatial mechanisms, shaft couplings, and robotics. Kenneth authored two classical books Mechanisms and Motion and Kinematic Geometry of Mechanisms, and co-authored the more modern text Robots and Screw Theory: Applications of Kinematics and Statics to Robotics. He was also one of the founding fathers, contributing to the foundation act with the initial member organizations, of the International Federation for the Theory of Machines and Mechanisms (in 1998 the official name was changed to IFToMM, acronym for the International Federation for the Promotion of Mechanism and Machine Science). The federation was officially born in 1969 and Kenneth served on the first Executive Council and was the founding chairman of the Australian Committee.

    更新日期:2020-01-15
  • Stage-by-phase multivariable combination control for centralized and distributed drive modes switching of electric vehicles
    Mech. Mach. Theory (IF 3.535) Pub Date : 2020-01-15
    Lipeng Zhang; Liuquan Yang; Xiaobin Guo; Xinmao Yuan

    This paper presents a new modes switching control method based on a dual-motor centralized and distributed coupling drive system, which can achieve the centralized and distributed coupling drive and reduce the modes switching shock to improve electric vehicle dynamics performance. Initially, the influence of the switching speed on the shock is analyzed and the models of each modes switching stage are established. Furthermore, a stage-by-phase multivariable combination controller based on the control of position, velocity and force of the actuators is designed, and a load torque state observer is developed to estimate system interference. Finally, the shock suppression effect is testified by the upshift process simulation and the experiments of a centralized and distributed coupling drive electric vehicle. The research shows that the peak value of the switching process with the controller is 9 m/s3, which is lower than the recommended value of 10 m/s3. It laid the theoretical foundation for solving the mode switching problem of the centralized and distributed coupling drive electric vehicles.

    更新日期:2020-01-15
  • A novel methodology for determining the singularities of planar linkages based on Assur groups
    Mech. Mach. Theory (IF 3.535) Pub Date : 2020-01-15
    Jianyou Han; Shengjie Shi

    In this paper, a simple and effective methodology for judging the singularities of planar linkages is presented, which is based on Assur groups. The methodology determines the geometrical configurations of the Assur groups in singularities. Based on the singularities of a simple two-bar group, the possible singularities of all Assur four-bar and six-bar groups are given by the concept of instant centers. Then the general process and rules of determining singularities are obtained and shown through several examples of the 1-DOF planar linkages. These linkages include the two six-bar linkages and the several eight-bar linkages composed of Assur six-bar groups. The singularities of them verify the proposed methodology, which reveals that the singularities of a linkage only depend on the Assur groups. Therefore, as long as the singularities of Assur groups are determined, all the possible singularities of the linkage composed of these groups can be determined. This methodology is independent of linkages, so it is universal for all planar multi-bar linkages which can be divided into these Assur groups.

    更新日期:2020-01-15
  • Methods for dimensional design of parallel manipulators for optimal dynamic performance over a given safe working zone
    Mech. Mach. Theory (IF 3.535) Pub Date : 2020-01-15
    Vimalesh Muralidharan; Ashwin Bose; Kishen Chatra; Sandipan Bandyopadhyay

    Two optimal design methods are proposed for the dimensional design of parallel manipulators, considering their dynamic performance over the desired ranges of motions, velocities, and accelerations. The first method, termed as the extrinsic method, directly minimises the actuator forces/torques within the desired safe working zone of the manipulator, for typical velocities and accelerations of the end-effector. The second method, namely, the intrinsic method, minimises a measure of the manipulator’s inertia, as reflected at the actuators, over the said safe working zone. Case studies on the design of 3-RRR and 3-RRS manipulators are presented to illustrate the proposed methods. Numerical studies show that the optimal link dimensions obtained through these conceptually disparate methods are fairly similar. Naturally, the dynamic performances of the resulting manipulators are also comparable, which are found to be significantly better than that of arbitrary designs respecting the same constraints.

    更新日期:2020-01-15
  • A variational simulation framework for the analysis of load distribution and radial displacement of cylindrical roller bearings
    Mech. Mach. Theory (IF 3.535) Pub Date : 2020-01-14
    Alexander Aschenbrenner; Benjamin Schleich; Stephan Tremmel; Sandro Wartzack

    In many technical systems, rolling bearings are critical machine elements concerning accuracy and lifetime. Their load distribution and radial displacement are directly linked to the accuracy and the fatigue life of rolling bearings. However, load distribution and radial displacement form a complex interdependency. Geometric deviations further influence this mutual connection. Although there are several approaches to determine the load distribution and the radial displacement, most of them are either too simplistic, allowing only the consideration of dimensional deviations, or too sophisticated and therefore unsuitable for a statistical evaluation of geometric deviations. Hence, the main purpose of this contribution is to provide a method for the determination of load distribution and radial displacement of cylindrical roller bearings that allows the consideration of geometric deviations as well as statistical evaluation of these deviations. Moreover, applying the method to a use case shows, whether the consideration of geometric deviations in the determination of load distribution and radial displacement is reasonable. The novelty of the contribution is, therefore, the provision of a statistical variational simulation framework for the analysis of load distribution and radial displacement of rolling bearings.

    更新日期:2020-01-15
  • Design and analysis of a configuration-based lengthwise morphing structure
    Mech. Mach. Theory (IF 3.535) Pub Date : 2020-01-15
    Jieyu Wang; Yinjun Zhao; Fengfeng Xi; Yingzhong Tian

    The ability of changing aircraft wing shape or geometry has drawn great attention of researchers in the past decades. This paper proposes a new approach to design a lengthwise morphing structure for an airfoil morphing wing. The structure is composed of n planar mechanism units. Each unit is designed to have 3 degrees-of-freedom (DOFs) that can be fully controlled by two actuators using lockable joints. This structure is reconfigurable through dual mode switching by locking specific joints. The end-effector of the mechanism can reach any desired position and the morphing wing can change to any desired shape. When locking three or four actuators, the structure turns into a statically determinate or indeterminate truss structure to withstand required loads. Force analysis for the structure during morphing motions is conducted based on statics, and an optimization method is used to determine the appropriate number of actuators and their placements. Prototypes with or without skins are fabricated to verify the feasibility of the design.

    更新日期:2020-01-15
  • Tangential intersection of branches of motion
    Mech. Mach. Theory (IF 3.535) Pub Date : 2020-01-15
    P.C. López-Custodio; A. Müller; X. Kang; J.S. Dai

    The branches of motion in the configuration space of a reconfigurable linkage can intersect in different ways leading to different types of singularities. In the vast majority of reported linkages whose configuration spaces contain multiple branches of motion the intersection happens transversally, allowing local methods, like the computation of its tangent cone, to identify different branches by means of their tangents. However, if these branches are of the same dimension and they intersect tangentially, it is not possible to identify them by means of the tangent cone at the singularity as the tangent spaces to the branches are the same. Although this possibility has been mentioned by a few researchers, whether linkages with this kind of tangent intersection of branches of motion exist is still an open question. In this paper, it is shown that the answer to this question is yes: A local method is proposed for the effective identification of branches of motion intersecting tangentially, and a method for the type synthesis of linkages that exhibit this particular type of singularity is presented.

    更新日期:2020-01-15
  • Development of an active and passive finger rehabilitation robot using pneumatic muscle and magnetorheological damper
    Mech. Mach. Theory (IF 3.535) Pub Date : 2020-01-14
    Daoming Wang; Yakun Wang; Bin Zi; Zixiang Cao; Huafeng Ding

    This paper presents the development of a finger rehabilitation robot (FRR) for active and passive training to fulfill the requirements of different rehabilitation stages. In the design, an antagonistic pair of pneumatic muscles (PMs) are utilized to exert a bidirectional force for passive training, and a controllable magnetorheological (MR) damper is used to provide a damping force for active training. In this paper, first, a detailed illustration of the mechanical design of the FRR, including the driving, transmission and actuating mechanisms, and the damping device, is presented. Subsequently, the kinematic analysis and simulation are described, followed by the static and dynamic analysis of the designed FRR. This paper details the static force transfer of the transmission mechanism, and the establishment of dynamic equations for the passive training system. Finally, an experimental set-up is established, and several passive and active training experiments are conducted for the performance evaluation of the FRR prototype. The results validate the feasibility and stability of the developed FRR.

    更新日期:2020-01-15
  • A geometrical approach for configuration and singularity analysis of a new non-symmetric 2DOF 5R Spherical Parallel Manipulator
    Mech. Mach. Theory (IF 3.535) Pub Date : 2020-01-13
    Alireza Alamdar; Farzam Farahmand; Saeed Behzadipour; Alireza Mirbagheri

    A new non-symmetric 5R-SPM is introduced and a geometrical approach is developed to analyze its configurations and singularities. The proposed methodology determines the type of configuration of a 5R-SPM, i.e. regular, singular, or out-of-workspace and also the type of singularity, i.e. instantaneous or finite, only based on geometric parameters and without solving verbose kinematic equations. It also provides insights into the workspace and singularities of 5R-SPMs, in the preliminary stage of design. The mechanism was analyzed by both the new geometrical approach and conventional methods for comparison. The geometrical approach could intuitively detect all the singularities observed by the Jacobian matrix and the kinematic analysis, with more details on the type and characteristics of each singularity. The dimensional synthesis for the designed mechanism was also performed based on the type and existence of singularities. The proposed methodology might be further developed to specify the configurations and singularities of general SPMs and also to introduce a geometrical measure for singularity closeness.

    更新日期:2020-01-14
  • Design of a helical gear set with adequate linear tip-relief leading to improved static and dynamic characteristics
    Mech. Mach. Theory (IF 3.535) Pub Date : 2020-01-13
    Zhi-Gen Wang; Yi-Cheng Chen

    This study aims to improve the static and dynamic characteristics of a helical gear pair by optimizing the parameters of linear tip-relief. The static analysis intends to reduce the maximum contact stress to extend the service life of the gear pair, while the dynamic analysis attempts to reduce the dynamic transmission error (DTE). First, mathematical models of a helical gear pair generated by rack-cutters with linear tip-relief were developed based on the theory of gearing. Tooth contact analysis enabled us to estimate static transmission error and contact pattern of the gear pair under various assembly errors. Additionally, the contact stress contour and mesh stiffness were calculated through loaded tooth contact analysis by using finite element analysis. A dynamic model of the helical gear pair was also developed to simulate the dynamic characteristics under various rotational speeds, including DTE and vibration energy. Finally, the simulation results revealed that the high contact stress, DTE, and vibration energy of the original helical gear set were successfully reduced by the improved linear tip-relief parameters.

    更新日期:2020-01-14
  • Inverse displacement analysis of a novel hybrid humanoid robotic arm
    Mech. Mach. Theory (IF 3.535) Pub Date : 2020-01-13
    Peng Sun; YanBiao Li; ZeSheng Wang; Ke Chen; Bo Chen; Xi Zeng; Jun Zhao; Yi Yue

    The application of hybrid mechanisms in the field of humanoid robots has attracted significant attention. A novel eight-degree-of-freedom hybrid manipulator is proposed to realize a kinematic function similar to that of the human arm. A general method for solving the inverse displacement problem of hybrid mechanisms is given, and the proposed humanoid robotic arm is taken as an example to demonstrate the solution process of this method. Furthermore, a closed-form solution for the inverse displacement problem of the hybrid humanoid robotic arm is derived by using the given method based on screw theory, exponential product formula, and Paden–Kahan subproblems. In addition, the problem of verifying and selecting the appropriate solutions according to the starting postures is also illustrated in a series of simulation experiments. Simulation experiment results show that there are (at most) 32 sets of solutions for the proposed humanoid robotic arm according to the same target position-orientation matrix and the given redundant input variables, and the accuracy of the proposed method for solving the inverse displacement problem is verified.

    更新日期:2020-01-14
  • A new Bricard-like mechanism with anti-parallelogram units
    Mech. Mach. Theory (IF 3.535) Pub Date : 2020-01-13
    Xuemin Sun; Ruiming Li; Zhiyuan Xun; Yan-An Yao

    This paper proposes a new Bricard-like mechanism composed of three anti-parallelogram units. First, the configuration and connection of the Bricard-like mechanism are given. Second, the mechanism is simplified as a spatial single-loop overconstrained 6R mechanism with variable links’ lengths and its Denavit-Hartenberg (D-H) parameters are obtained by identifying the six revolute joints axes. Third, the degree of freedom of the mechanism is calculated through the closure equations, and kinematic paths of output variables are plotted with respect to the input variable. Then, a serial of Bricard-like mechanisms are connected to construct the deployable mechanism. Finally, three prototypes of the Bricard-like mechanism and the triangular prism deployable mechanism composed of four Bricard-like mechanisms are designed and fabricated to verify the feasibility of the proposed method and analysis.

    更新日期:2020-01-13
  • Total variation on horizontal visibility graph and its application to rolling bearing fault diagnosis
    Mech. Mach. Theory (IF 3.535) Pub Date : 2020-01-13
    Yiyuan Gao; Dejie Yu

    The total variation on graph (TVG) is a powerful vertex domain index for measuring the smoothness of graph signals, but its performance is closely related to the underlying graph. Since the horizontal visibility graph can better reflect the dynamics characteristics of bearing vibration signals than the path graph, the underlying graph of TVG is designated as horizontal visibility graph. The vertex domain index TVG defined on horizontal visibility graph is called simply as TVHVG in this paper. For better distinguishing the different states of rolling bearings, the bearing vibration signal is converted into the graph signal indexed by its horizontal visibility graph, and the vertex domain index TVHVG is extracted as the single fault feature. Based on TVHVG feature extraction and Mahalanobis distance classification, a novel fault diagnosis method for rolling bearings is proposed. The proposed method is applied to analyze two sets of experimental data containing normal and faulty rolling bearings. The results indicate that the proposed method can diagnose the bearing faults with different types and degrees effectively, and the vertex domain index TVHVG is superior to some classical time domain indexes in distinguishing the different states of rolling bearings.

    更新日期:2020-01-13
  • Type synthesis of overconstrained 2R1T parallel mechanisms with the fewest kinematic joints based on the ultimate constraint wrenches
    Mech. Mach. Theory (IF 3.535) Pub Date : 2020-01-13
    Yundou Xu; Yun Zhao; Yi Yue; Fengfeng Xi; Jiantao Yao; Yongsheng Zhao

    “Two rotational degrees of freedom” and “one translational degree of freedom” (2R1T) parallel mechanisms (PMs) have been successfully applied to develop five-axis hybrid robots for machining purposes. However, the number of passive joints contained in current 2R1T PMs has not still reached the minimum, which may impede these robots from having high stiffness. This study has put forward the concept of ultimate constraint wrenches acting on the PM's moving platform, and this concept was used to reduce the number of kinematic joints to a minimum. Based on the reciprocal screw theory, an ultimate constraint wrench system of the 2R1T PMs was found, and then a series of novel overconstrained 2R1T PMs with the fewest kinematic joints, containing three or four branches, were constructed. Furthermore, based on a developed overconstrained four-branch 2R1T PM RPU-2UPR-RPR, a type of five-axis hybrid robot with the fewest kinematic joints was constructed, which demonstrated good application prospects.

    更新日期:2020-01-13
  • Study on load sharing behavior of coupling gear-rotor-bearing system of GTF aero-engine based on multi-support of rotors
    Mech. Mach. Theory (IF 3.535) Pub Date : 2020-01-13
    Siyu Wang; Rupeng Zhu; JinFeng

    Based on the multi-support mode of low-pressure rotor and fan rotor of gearbox in GTF (Geared turbofan engine), the coupling gear-rotor-bearing dynamics model is established in this paper. The effect of bearings on both rotors on the dynamic behavior of the GTF transmission system have been explored and quantified, especially for the influence of location of bearings on both rotors on the load sharing behavior of the star gearing system in GTF gearbox. Axial, transverse and rotational motions of double-helical gears are included in the dynamic model, in which the time-varying support stiffness of bearings, the gear mesh stiffness with phase relationship between multiple meshes and comprehensive errors are fully considered. The results show that position of bearings on both rotors could affect the load sharing performance and maximum floating amounts of members in star gearing system of GTF gearbox, therefore, the location of bearings on rotors can be rearranged to achieve better performance in vibration control and load distribution of the system.

    更新日期:2020-01-13
  • Control of MIMO mechanical systems interacting with actuators through viscoelastic linkages
    Mech. Mach. Theory (IF 3.535) Pub Date : 2020-01-13
    M.R. Homaeinezhad; S. Yaqubi; H.M. Gholyan

    This paper proposes a new method for control of nonlinear multi input – multi output (MIMO) mechanical systems that incorporate viscoelastic dampers (VED) for reducing undesired vibrations of actuators. To this end, a control algorithm is proposed based on considering various characteristics of the described dynamical systems (namely mechanical dynamics, viscoelasticity and actuator dynamics) in generation of control inputs guaranteeing convergence of system response to desired reference signals. This procedure features three consecutive parts within the control loop which are conducted iteratively at each control sample. At each sample, initially necessary forces and moments exerted to mechanical system are calculated as virtual control inputs generated based on a MIMO discrete-time sliding mode control (DSMC) algorithm. As the aim of control model is obtaining a closed-loop system without resulting in notable vibrational effects, undesired chattering effects should be eliminated from inputs generated by DSMC. This objective is attained by calculation of appropriate input bounds. Next, an additional virtual input is assigned corresponding to viscoelastic strain such that virtual mechanical input from previous part of the control loop is generated. To this end, Maxwell model for viscoelastic material is considered. Finally, actual controller input is generated such that all virtual control objectives are satisfied. The effectiveness of control procedure is numerically illustrated for a 3-PRR manipulator.

    更新日期:2020-01-13
  • Elastodynamic analysis of a novel motion-decoupling forging manipulator
    Mech. Mach. Theory (IF 3.535) Pub Date : 2020-01-13
    Yundou Xu; Zhicheng Teng; Jiantao Yao; Yulin Zhou; Yongsheng Zhao

    The forging manipulator is a complex industrial robot with a spatial serial-parallel hybrid structure and multiple degrees of freedom, and the decoupling ability among different motions is a critical performance index for it. A novel kind mechanism of forging manipulator that can achieve decoupling between lifting and horizontal buffering motions was proposed, by integrating the improved Hoeckens straight-line mechanism with the buffering mechanism. It is easy to realize motion control of such forging manipulator, which indicates that it has potential application prospects. Considering the motion-decoupling characteristics as well as the practical working conditions, the whole architecture of this novel forging manipulator was divided into three independent single-degree-of-freedom sub-mechanisms. Then, with the elastic deformations of each component taken into consideration, the elastodynamic model of each sub-mechanism based on the finite element theory and the KED (Kineto-Elastodynamic) analysis was established for more accurate dynamic responses. The Newmark stepwise integration method was used to solve the elastodynamic equations, and the response characteristics of displacement, velocity, and acceleration of the manipulator were obtained, providing important theoretical references for further optimization designs and practical applications of this novel mechanism for forging manipulators.

    更新日期:2020-01-13
  • Kinetostatic modeling and characterization of compliant mechanisms containing flexible beams of variable effective length
    Mech. Mach. Theory (IF 3.535) Pub Date : 2020-01-13
    Fulei Ma; Guimin Chen

    Flexible beams of variable effective length, serve both transmission and actuation functionalities in compliant mechanisms, have been employed in many devices, e.g., thermal actuators and continuum robots. This difunctional feature is favorable when utilized for operations in confined space. However, the length variation introduces modeling difficulties, which poses a new challenge to designers. To accurate model flexible beams of variable effective length and characterize the behaviors of associated compliant mechanisms form the primary objectives of this study. The chained beam constraint model is revisited and extended to model beams of variable effective length. Modeling of a chevron shape thermal in-plane microactuator and a continuum mechanism are provided to demonstrate the effectiveness of the proposed method. The predicted results have a high degree of accuracy as compared to experimental results and nonlinear finite element results.

    更新日期:2020-01-13
  • Novel block mechanism for rolling joints in minimally invasive surgery
    Mech. Mach. Theory (IF 3.535) Pub Date : 2020-01-13
    Jeongryul Kim; Seong-il Kwon; Keri Kim
    更新日期:2020-01-13
  • Dynamic analysis of a bevel gear system equipped with finite length squeeze film dampers for passive vibration control
    Mech. Mach. Theory (IF 3.535) Pub Date : 2020-01-13
    Weitao Chen; Siyu Chen; Zehua Hu; Jinyuan Tang; Haonan Li

    Though finite length squeeze film dampers (FLSFD) are practically and effectively applied to vibration attenuation, they have not been popularly used in bevel gear systems (BGS) due to the limitations of the existing models of FLSFD. The present work proposes a general approach for modeling and calculating the nonlinear oil-film force of FLSFD, which is introduced into system motion equations to model the BGS supported on FLSFD mathematically. Comparisons with conventional methods show the superiorities of the proposed model in terms of computational accuracy and versatility. The damping characteristics of FLSFD are examined by comparing the dynamic behaviors of the BGS with and without FLSFD. Besides, the response sensitivity of the system to different parameters, including the length and radial clearance of FLSFD, is also discussed. The results show that FLSFD can significantly reduce the vibration amplitude passing through the critical speeds and suppress the nonlinear characteristics of the system, such as bistable state responses and jump phenomena. The results also reveal a dependence of the damping performance on the choice of the FLSFD design parameters.

    更新日期:2020-01-13
  • Probabilistic safety model and its efficient solution for structure with random and interval mixed uncertainties
    Mech. Mach. Theory (IF 3.535) Pub Date : 2020-01-13
    Jiaqi Wang; Zhenzhou Lu

    Random and interval mixed uncertainties (RIMU) universally exist in engineering, thus it is necessary to construct a reasonable model for analyzing the probabilistic safety degree in this case. Aiming at analyzing the probabilistic safety degree efficiently, the existing double-loop nested optimization (DLNO) algorithm for estimating the upper and lower bounds of failure probability (FP) is firstly investigated under RIMU. It is proved that the upper and lower bounds of FP obtained by DLNO actually equal to the maximum and minimum of all approximate FPs with respect to the possible discrete points of interval variables. Secondly, it is found that the failure domain corresponding to the upper bound of FP is similar to that of time-dependent reliability under random uncertainty. Based on this similarity, the inequality relations are established for the real upper and lower bounds of FP and those obtained by DLNO, and the Kriging surrogate model methods are proposed to solve probabilistic safety model under RIMU efficiently. Additionally, this efficient solution strategy is further extended to the time-dependent structure under RIMU. Finally, numerical and engineering examples are used to demonstrate the reasonability and efficiency of proposed methods.

    更新日期:2020-01-13
  • Parametric design and regenerative braking control of a parallel hydraulic hybrid vehicle
    Mech. Mach. Theory (IF 3.535) Pub Date : 2019-12-05
    Shilei Zhou; Paul Walker; Nong Zhang

    Hydraulic hybrid technologies improve the fuel economy of city-use medium duty vehicles by recovering braking energy and reusing it for driving, most notably vehicle launching. In this paper, a parametric design of hydraulic driving system for a medium duty truck is conducted based on its power demand in typical urban driving cycles. The braking control strategy is designed considering both the safety regulations and braking energy recovery rate. The proportional relationship of hydraulic pump/motor output torque and its working pressure is considered when designing the braking control strategy. The influence of the high pressure accumulator minimum working pressure and the corresponding gas volume at the minimum pressure on the braking energy recovery rate is analyzed. The simulation results show that the proposed hydraulic driving system and braking control strategy helps greatly increase the braking energy recovery rate. Besides, different vehicle mass and load distributions are investigated to analyze the regenerative braking effect on various loading conditions.

    更新日期:2020-01-04
  • Dynamic transition trajectory planning of three-DOF cable-suspended parallel robots via linear time-varying MPC
    Mech. Mach. Theory (IF 3.535) Pub Date : 2019-12-04
    Sheng Xiang; Haibo Gao; Zhen Liu; Clément Gosselin

    This paper presents a dynamic transition trajectory planning technique for fully-actuated three-degree-of-freedom cable-suspended parallel robots. The proposed two-step technique can be used to plan transition trajectories to general periodic motions that extend beyond the static workspace of the mechanism. In the first step, the robot dynamics are linearized and partly decoupled by handling the less restricted gravity axis trajectory planning problem. The corresponding dynamic model and constraints of the other axes then become linear time-varying. Secondly, the generation of general periodic trajectories and the general transition trajectories is accomplished by convex optimization. The formulation of a constrained linear-quadratic optimal control problem for the dynamic transition task shows essential differences from previous works and extends to general cases. The proposed technique has the ability to generate general periodic trajectories and provides a universal transition planner. Indeed, there is no need to rely on a specific amplitude increment function, which makes the planning technique more flexible and applicable to general cases. Moreover, the quadratic programming problems can be solved reliably and rapidly. Example transition trajectories to harmonic and to non-harmonic periodic trajectories are given in order to illustrate the approach.

    更新日期:2020-01-04
  • A four-limb parallel Schönflies motion generator with full-circle end-effector rotation
    Mech. Mach. Theory (IF 3.535) Pub Date : 2019-12-04
    Guanglei Wu; Zirong Lin; Wenkang Zhao; Sida Zhang; Huiping Shen; Stéphane Caro

    This paper presents a four-limb parallel Schönflies motion generator for the pick-and-place application, whose end-effector is composed of a planetary gear train as the amplification mechanism to realize the full-circle rotation. The kinematic aspects, including the workspace, dexterity and singularity, are analyzed and evaluated. The singular configurations and the singularity loci are identified both graphically and numerically, which shows that the singular configurations of the manipulator can be avoided by keeping all the limbs working in a prescribed working mode together with the end-effector rotation in a clockwise direction from the neutral orientation. Moreover, the dexterity evaluation is carried out to depict the workspace quality and dexterous working envelope. It turns out that the proposed robot admits a super-ellipsoidal workspace with the full-circle rotation of the end-effector, suitable for pick-and-place operations. Finally, robot dynamics is considered to select the actuators.

    更新日期:2020-01-04
  • Orthodiagonal anti-involutive Kokotsakis polyhedra
    Mech. Mach. Theory (IF 3.535) Pub Date : 2019-12-26
    Ivan Erofeev; Grigory Ivanov

    We study the properties of Kokotsakis polyhedra of orthodiagonal anti-involutive type. Stachel conjectured that a certain resultant connected to a polynomial system describing flexion of a Kokotsakis polyhedron must be reducible. Izmestiev [3] showed that a polyhedron of the orthodiagonal anti-involutive type is the only possible candidate to disprove Stachel’s conjecture. We show that the corresponding resultant is reducible, thereby confirming the conjecture. We do it in two ways: by factorization of the corresponding resultant and providing a simple geometric proof. We describe the space of parameters for which such a polyhedron exists and show that this space is non-empty. We show that a Kokotsakis polyhedron of orthodiagonal anti-involutive type is flexible and give explicit parametrizations in elementary functions and in elliptic functions of its flexion.

    更新日期:2020-01-04
  • Design and optimization of a lightweight and compact waist mechanism for a robotic rat
    Mech. Mach. Theory (IF 3.535) Pub Date : 2019-12-14
    Chang Li; Qing Shi; Zihang Gao; Mengchao Ma; Hiroyuki Ishii; Atsuo Takanishi; Qiang Huang; Toshio Fukuda

    A multi-degree-of-freedom (multi-DOF) waist mechanism is required for robotic rats to perform species-typical behaviors, but the existing waist mechanisms are heavy and cumbersome. To solve this problem, we propose a linkage-based slider-coupled symmetric swing (S3) mechanism, which features a single-input multiple-output structure, allowing it to couple multiple DOFs. The linkage mechanism has a variety of forms and linkage curves, making the S3 mechanism suitable for multiple-constraint optimization. Based on kinematic and dynamic analyses, we constrain the S3 mechanism in terms of bending angle, transmission angle, symmetry, and its existence, and then we optimize its dimensions using an interior-point method to make it compact. Compared with an existing waist mechanism, the proposed waist mechanism has only 47.8% of the weight and smaller dimensions, making it more lightweight and compact. Experiments on a robotic rat show that the proposed waist mechanism enables a robotic rat to perform rat-like upright rearing in 0.5s and tail grooming behavior in 0.4s, indicating its good biomimetic and dynamic performances. Comparisons between two generation robotic rats also reveal that the robot with new waist mechanism has similar (sometimes superior) pitching and bending abilities with the former one.

    更新日期:2020-01-04
  • Multi-objective optimization of hypoid gears to improve operating characteristics
    Mech. Mach. Theory (IF 3.535) Pub Date : 2019-12-17
    Vilmos V. Simon

    In this paper a multi-objective optimization method of hypoid gears correlating to the operating characteristics is presented. Optimal design of hypoid gears demands that multiple objectives be simultaneously achieved. Four objectives considered in this study are the minimization of the maximum tooth contact pressure, transmission error and the average temperature in the gear mesh, and the maximization of the mechanical efficiency of the gear pair. The goals of the optimization are achieved by the optimal modification of meshing teeth surfaces. In practice, these modifications are introduced by applying the appropriate machine tool setting for the manufacture of the pinion and the gear, and/or by using a tool with an optimized profile. The proposed optimization procedure relies heavily on the loaded tooth contact analysis for the prediction of tooth contact pressure distribution and transmission errors, and on the mixed elastohydrodynamic analysis of lubrication to determine temperature and efficiency. A fast elitist nondominated sorting genetic algorithm (NSGA-II) is applied to solve the model. The effectiveness of the method is demonstrated by using hypoid gear examples. The obtained results have shown that by the optimization considerable improvements in the operating characteristics of the gear pair are achieved.

    更新日期:2020-01-04
  • Novel design method for nonlinear stiffness actuator with user-defined deflection-torque profiles
    Mech. Mach. Theory (IF 3.535) Pub Date : 2019-12-17
    Xiuqi Hu; Zhibin Song; Tianyu Ma

    In this paper, a novel design method for compact nonlinear stiffness actuator (NSA) is proposed. By combining cam with off-the-shelf torsion spring and designing the effective profile curve of cam, the proposed NSA can perform desired bidirectional symmetric deflection-torque profiles with monotonic increasing slopes that follow the “low load, low stiffness and high load, high stiffness” principle inspired by biomechanics. To adapt to external loads in different directions, the proposed NSA is designed to have bidirectional symmetric stiffness characteristics by using symmetrical cams and mutilated gear transmission. The derivation process of the effective cam profile curve is introduced in detail. And then, a prototype of the designed NSA is built for verification. Simulated and experimental stiffness tests demonstrate the effectiveness of the proposed design method in realizing desired nonlinear stiffness. Preliminary experiments of step response in controlling torque show good performance of the proposed NSA in terms of dynamic response.

    更新日期:2020-01-04
  • The influence of coordinates in robotic manipulability analysis
    Mech. Mach. Theory (IF 3.535) Pub Date : 2019-12-17
    Johannes Lachner; Vincenzo Schettino; Felix Allmendinger; Mario Daniele Fiore; Fanny Ficuciello; Bruno Siciliano; Stefano Stramigioli

    Coordinates play an essential role in the description of real world objects and physical processes. In robotics, coordinates are used to describe the kinematic structure and the kinematic and dynamic behavior. The description mostly takes place in charts, assigned by the observer of the robotic system. However, it is crucial that the described physical process does not depend on the coordinate choice of the observer. In this work we show the relation between coordinates and manipulability analysis. Manipulability measures are dependent of joint coordinates of the robot and task coordinates in the workspace of the robot. Both relations can be analyzed with tensor geometry. We remove the dependency on joint coordinates through the use of an appropriate metric. With the help of tensor contraction, the resulting induced metric in the workspace can be transformed into a coordinate invariant matrix. After applying eigenvalue decomposition on this matrix, we can visualize the dynamic manipulability of a robot as a coordinate invariant ellipsoid.

    更新日期:2020-01-04
  • A novel algorithm for the isomorphism detection of various kinematic chains using topological index
    Mech. Mach. Theory (IF 3.535) Pub Date : 2019-12-18
    Tao Deng; Hui Xu; Peng Tang; Ping Liu; Li Yan

    For mechanism design, the isomorphic kinematic chains (KCs) should be deleted to improve design efficiency. At present, most methods of isomorphism detection involve complex concepts and comparison of intermediate parameters. Moreover, when the number of components increases, it is complex and difficult to discriminate a large number of KCs in short time. However, the molecular topological index is proposed to identify isomer in organic chemistry, which shows excellent abilities for isomer recognition. In some respects, topological graph of kinematic chain is similar to chemical molecular model. Therefore, this idea is adopted to obtain extended adjacency identification index (EAID) which fits for isomorphism detection of KCs, namely KC-EAID. If two topological graphs have same KC-EAID value, then they are isomorphic. Otherwise, they are not. Three kinds of kinematic chains, including simple joints KCs, multiple joints KCs and gear-link KCs are given to verify effectiveness of this index in isomorphism detection. For KC-EAID index, it requires a few known quantities and no comparison of intermediate parameters. The algorithm only includes the calculation of matrices, which saves operation time. Therefore, KC-EAID can be used as a powerful tool for isomorphism detection in number synthesis of KCs.

    更新日期:2020-01-04
  • On the relation between vane geometry and theoretical flow ripple in balanced vane pumps
    Mech. Mach. Theory (IF 3.535) Pub Date : 2019-12-18
    Mattia Battarra; Emiliano Mucchi

    Advancements related to the correlation between pump design parameters and the kinematic flow ripple in balanced vane pumps are addressed in the present work. In particular, the study focuses the attention on the influence of the vane geometry on the oscillations of the flow rate produced by the volume variation of both under-vane pockets and displaced chambers, that is known as one of the most relevant sources of noise in hydraulic systems. The working principle of the machine is detailed and used as starting point to deduce analytical correlations describing both vane kinematics and delivery flow rate ripple. The set of results that can be achieved with the obtained formulation is evaluated by means of a nondimensional parametric study including the two main design parameters defining the vane geometry, i.e. thickness and tip radius. The resulting trends demonstrate that the theoretical delivery flow ripple is closely related to the vane design and the cam ring shape profile.

    更新日期:2020-01-04
  • An MPC-based two-dimensional push recovery of a quadruped robot in trotting gait using its reduced virtual model
    Mech. Mach. Theory (IF 3.535) Pub Date : 2019-12-23
    Navid Dini; Vahid Johari Majd

    This paper addresses the push recovery of quadruped robots trotting on even terrain. Push recovery is the ability of a legged robot to maintain its balance in the presence of sudden external forces applied to the robot. Due to the nature of this dynamical gait, the quadruped robot can be modeled as a biped robot where each two cross legs of the quadruped are modeled as a virtual leg. Then, the virtual biped model is further reduced to a two-dimensional linear inverted pendulum plus flywheel model (LIPFM). Moreover, using the concept of capture points for the biped model, the desired locations for the center of pressure (COP) of the legs for recovering the robot's balance are calculated by designing a two-dimensional dynamic capture point estimator. A model-based predictive controller (MPC) is then proposed to adjust the footstep locations and generate a new walking-pattern. The resulting redesigned joint angles for the virtual biped model are then transformed back to those of the actual quadruped model. Simulation results show the effectiveness of the proposed method.

    更新日期:2020-01-04
  • Investigation of the effects with linear, circular and polynomial blades on contact characteristics for face-hobbed hypoid gears
    Mech. Mach. Theory (IF 3.535) Pub Date : 2019-12-20
    Chengcheng Liang; Chaosheng Song; Caichao Zhu; Siyuan Liu; Xingyu Yang

    On this research, the effects of the three different types of blade sections including linear, circular and polynomial on mesh characteristics for face-hobbed hypoid gears are investigated. Firstly, with the equations of three blade sections and the transformation matrixes based on the processing method derived, the mathematical model of gear flank and loaded finite element mesh model are proposed. Then, the impacts of different blade sections on tooth surface deviation and mesh characteristics are analyzed. Results show that the effects are almost identical when the parameters choose reasonable for the three blades. However, with the circular radius reducing, the peak-to-peak value of transmission error decreases but the contact pattern area shrinks and the location of maximum bending stress will change. For the polynomial blade, the effects the design parameters on mesh characteristics are obvious.

    更新日期:2020-01-04
  • Fundamental equation of mechanism kinematic geometry: Mapping curve in se(3) to counterpart in SE(3)
    Mech. Mach. Theory (IF 3.535) Pub Date : 2019-12-23
    Leilei Zhang; Yanzhi Zhao; Tieshi Zhao

    The most general continuous rigid motion can be described by a curve in SE(3) of whose tangent vector the left or right invariant representation is a curve in se(3). The integral operation between them has not been achieved because there is no general solution for a system of the first-order linear differential equations with variable coefficients in mathematics. This paper develops a matrix equation (termed as the fundamental equation) based on the geometric properties of a pair of conjugate axodes equivalent to a curve in se(3) in algebras to achieve this integral operation. Moreover, the first-order and second-order derivations of the fundamental equation are derived. Furthermore, an algebraic method representing the body and spatial velocity twists as vector functions of dimensions and input parameters of mechanisms is founded on the theory of reciprocal screws. After that, this method and the fundamental equation are validated by the numerical examples of Bennett, spherical and planar four-bar linkages. Finally, this work presents a notion of generalized-involute which is a useful tool in the study of gear tooth profile and cam profile.

    更新日期:2020-01-04
  • 更新日期:2020-01-04
  • Singularity analysis of some multi-platform mechanisms by decomposition and reciprocality
    Mech. Mach. Theory (IF 3.535) Pub Date : 2019-12-20
    Michael Slavutin; Yoram Reich

    A singularity analysis of multi-platform parallel mechanisms is presented. If the mechanism can be decomposed into minimal mechanisms, the decomposition is performed and its singularity is determined through the singularity of its components. In contrast, if the mechanism is already a minimal mechanism, its singularity is determined through reduction of the original mechanism to a simpler mechanism using the reciprocality relation. The analysis of general two-platform and three-platform minimal mechanisms is presented, while examples of reduction to a simpler mechanism are shown on two actual two-platform mechanisms. It is found that for three-platform mechanisms, there are irreducible cases.

    更新日期:2020-01-04
  • Synthesis and analysis method for powertrain configuration of single motor hybrid electric vehicle
    Mech. Mach. Theory (IF 3.535) Pub Date : 2019-12-20
    Hang Peng; Datong Qin; Jianjun Hu; Chunyun Fu

    Existing hybrid powertrain configuration analysis methods mainly focus on power-split hybrid electric vehicles with multiple planetary gears. However, these methods cannot be applied directly to single motor hybrid electric vehicles with automatic transmission. Hence, an analysis method to optimize the powertrain configuration of single motor hybrid vehicles is proposed to overcome this limitation. In the proposed method, two different adjacency matrices are established to generate all powertrain configurations, and a corresponding matrix analysis method is proposed to analyze their working modes. Subsequently, a set of working modes are established to improve the efficiency of obtaining mathematical models of powertrain configurations. Finally, an energy management strategy based on dynamic programming is developed to analyze the performance of the generated configurations. The proposed method is utilized to analyze the single motor hybrid vehicle with a planetary gear and a continuously variable transmission, and a new configuration is obtained after the analysis for validation. It is observed that the fuel efficiency increases by 12.2% and the 0–100 km/h acceleration time is reduced by 8.7%, in comparison to the existing powertrain configuration.

    更新日期:2020-01-04
  • Topology optimization of compliant mechanism considering actual output displacement using adaptive output spring stiffness
    Mech. Mach. Theory (IF 3.535) Pub Date : 2019-12-20
    Min Liu; Jinqing Zhan; Benliang Zhu; Xianmin Zhang

    This paper presents a new method for topology optimization of compliant mechanisms considering actual output displacement. The optimization problem is reformulated by maximizing the output displacement with artificial springs meanwhile optimizing the actual output displacement without artificial springs to the prescribed value. A method of adaptive output spring stiffness is developed for automatic adjustment of output spring stiffness according to the prescribed actual output displacement. The multi-objective design problem is converted into a single-objective problem using the weighted-sum method and a weighting factor with adaptive adjustment is presented. This method is implemented based on the SIMP (Solid Isotropic Material with Penalization) formulation and the design problem is solved by the MMA (Method of Moving Asymptotes) optimization algorithm on the basis of the sensitivity analysis. Numerous numerical examples are applied to illustrate the effectiveness of the presented method.

    更新日期:2020-01-04
  • Mobility analysis of multi-configuration Rubik's Cube mechanism based on the reciprocal screws
    Mech. Mach. Theory (IF 3.535) Pub Date : 2019-12-20
    Daxing Zeng; Shuiyu Sun; Wenjuan Lu; Ming Li; Yulei Hou; Xueling Luo

    This paper focuses on the establishment of the kinematic diagram and the mobility of Rubik's Cube. Owing to the complex and variable characteristics of Rubik's Cube mechanism, a method of separating the inner and outer loops of Rubik's Cube mechanism and analyzing the Rubik's Cube with 1/8 module as a unit is proposed. Based on the topological graph and adjacency matrix, the kinematic diagram of Rubik's Cube unit which is in the first octant in both aligned and non-aligned states is constructed. On this basis, an analytical method for mobility due to the characteristics of strong coupling between the loops is proposed which is to separate the constraint of the internal and external of the mechanism, to successively decompose the mechanism by layer, then to process the front and back basic loops in proper order. Besides, a method is proposed to classify the sub-pieces and to decompose the coupling loops according to the direction of motion and the directed graph. Based on the screw theory and the “modified K-G formula”, the mobility of Rubik's Cube is obtained when it is in aligned and non-aligned states. Further, the theoretical analysis results are verified by the ADAMS.

    更新日期:2020-01-04
  • Structural analysis of ancient Chinese wooden locks
    Mech. Mach. Theory (IF 3.535) Pub Date : 2019-12-27
    Kan Shi; Kuo-Hung Hsiao; Yang Zhao; Chin-Fei Huang; Wen-Yi Xiong

    Humans all around the world have used locks for thousands of years. Wooden locks were the earliest locks in ancient China and were firmly fixed to the door. There are two principal types: bolt locks and pin tumbler locks. The original bolt lock was made with a thick bolt and the door. It could only be opened from the inside of the door. Improved continuously, a large number of wooden locks with different structures were invented. This work presents a systematic analysis of the structures of ancient Chinese wooden locks. The characteristics and the representations of wooden locks are described. There are totally 10 types of wooden locks that are presented as examples to demonstrate the operation processes. According to the insertion position of the key, Chinese wooden locks can be divided into seven types: no entry, bolt entry, case side entry, case bottom entry, case top entry, case front entry, and multiple entries. Ancient Chinese wooden locks come in various types with different ingenious designs, fully demonstrating the work of the highly skilled artisans in ancient Chinese society.

    更新日期:2020-01-04
  • Development of trajectory and force controllers for 3-joint string-tube actuated finger prosthesis based on bond graph modeling
    Mech. Mach. Theory (IF 3.535) Pub Date : 2019-12-30
    Neeraj Mishra; Anand Vaz

    The bond graph modeling and simulation of a redundant underactuated three-joint string-tube based prosthetic finger mechanism in the unlike configuration, for a class of prosthesis for a partially impaired hand, was presented for the implementation of the concept of opposition space for prehensile tasks. This work is its extension and systematically develops the structural basis and models for trajectory and force control schemes. The models emulate the abstract virtual domain of the intended task and the Central Nervous System (CNS), which provides control commands to the natural active finger joints, for the tracking control of desired position and force trajectories. The model for force control tracking has been developed systematically by utilizing the concept of causality from the bond graph model, where the motion of an infinitesimal mass is used as a trajectory input command for the generation of the desired force at the fingertip-object interface. The control models derived from their respective bond graphs do not require inverse kinematics to be worked out, and have been validated through simulations.

    更新日期:2020-01-04
  • Robust control algorithm using time delay estimation for speed mode of twisted string actuator
    Mech. Mach. Theory (IF 3.535) Pub Date : 2019-12-28
    Hyoryong Lee; Hyunchul Choi; Joowon Park; Sukho Park

    Twisted string actuators (TSAs) have been used where conversion of the rotational motion of a motor into a translatory motion by twisting two strings to control the length of the actuator is needed, e.g., in robot applications. Speed mode TSA (SM-TSA) improves the translatory motion achieved in previous TSAs by adding a shaft between two strings. However, the nonlinear response of the translatory displacements remains a problem. Modeling has been one approach, but payload changes or disturbances make it difficult to solve the nonlinear response of SM-TSA through modeling. Here, proportional–integral–derivative (PID) control and time delay control (TDC) in SM-TSA are evaluated as feedback mechanisms during translatory displacements. By following the desired trajectory through PID control and TDC under conditions of payload changes and spring disturbances in SM-TSA and evaluating tracking results, we show that both control methods can provide somewhat precise positional control in SM-TSA even if there are payload changes or spring disturbances. However, TDC shows smaller tracking errors and yields more robust performance against payload changes and disturbances compared to PID control.

    更新日期:2020-01-04
  • 更新日期:2020-01-04
  • Energy performance analysis of a suspended backpack with an optimally controlled variable damper for human load carriage
    Mech. Mach. Theory (IF 3.535) Pub Date : 2019-12-30
    Lianxin Yang; Jiwen Zhang; Yuning Xu; Ken Chen; Chenglong Fu

    This paper investigates the energy performance of human load carriage with a variable damped suspended backpack. A vertical double-mass coupled-oscillator model is adopted to predict the load movement and energy consumption. Optimal control is found to be bang-bang, switching four times between the minimum and the maximum damping in a step cycle. With analytically tested laws for optimal switching timing, an orbitally stable event-based control strategy with feedback is designed. Simulation results reveal that the suspended backpack with an optimally controlled variable damper improves the energy efficiency of load carriage and reduces the load force exerting on carriers for a wide range of suspension stiffness and walking conditions, representing less energy expenditure, better comfort and stronger adaptability over the passive elastic backpacks with constant suspension parameters. The working principle of the variable damper is also analyzed. Although this paper only deals with the theoretical model and analysis of the problem, the discussion on validity implies a considerable improvement in energy performance, including efficiency and adaptability.

    更新日期:2020-01-04
  • A recursive algorithm for dynamics of multiple frictionless impact-contacts in open-loop robotic mechanisms
    Mech. Mach. Theory (IF 3.535) Pub Date : 2019-12-28
    M. Ahmadizadeh; A.M. Shafei; M. Fooladi

    In this paper, the phenomenon of multiple impact-contacts has been dynamically modeled for an open kinematic chain with rigid links and revolute joints. The dynamic equations of the mentioned system have been extracted based on the recursive Gibbs–Appell formulation. The impact-contact phenomenon has been formulated by the regularized method in which the force of impact is a continuous function of the relative penetration and relative velocity of two colliding surfaces with respect to each other. The geometrical specifications and the mechanical properties of colliding surfaces are the two main parameters used in the modeling of viscoelastic contact force models. In this work, a recursive algorithm, which has been developed based on 3 × 3 rotation matrices to reduce the computational load, symbolically derives the motion equations of a multibody system that collides with surrounding surfaces at several points. The system under study includes the non-impact (flight) phase and the impact phase. Going from the flight phase to the impact phase and back, detecting the exact moment of impact, and also solving the differential equations of motion during a very short impact time have their particular challenges and complexities, which are dealt with in this work. In the next step, nine famous contact force models have been compared in order to select the most suitable model for simulation work. Finally, to show the accuracy and the capability of the presented algorithm, the dynamic behavior of an open-chain robotic mechanism consisting of 4 rigid links connected by revolute joints has been simulated and analyzed.

    更新日期:2020-01-04
  • 更新日期:2020-01-04
  • Design of a six-DOF motion tracking system based on a Stewart platform and ball-and-socket joints.
    Mech. Mach. Theory (IF 3.535) Pub Date : 2019-05-18
    Kim Yong-Sik,Hongliang Shi,Nicholas Dagalakis,Jeremy Marvel,Geraldine Cheok

    This paper presents a six degree-of-freedom (DOF) real-time motion tracking system of measuring the position and the orientation for industrial robots in three-dimensional (3D) space. The proposed system is based on a typical Stewart platform design and utilizes six low-cost displacement sensors to monitor the motion of the Stewart platform. The advantage of the proposed system is its simple calibration and easy accessibility; the magnetic ball-and-socket joints used for rotational joints. With special measurement tools, the center of rotation of all twelve joints can be measured in 3D space at a glance. Following more than fifty measurements, the average root mean square (RMS) position accuracy error of the proposed device is less than 0.186 mm and the average of angular accuracy error is less than 0.160 °, making it suitable for monitoring the performance of industrial robot. A commercial robot is also tested by the proposed system to verify its usefulness.

    更新日期:2019-11-01
  • Correcting Duporcq's theorem.
    Mech. Mach. Theory (IF 3.535) Pub Date : 2014-12-30
    Georg Nawratil

    In 1898, Ernest Duporcq stated a famous theorem about rigid-body motions with spherical trajectories, without giving a rigorous proof. Today, this theorem is again of interest, as it is strongly connected with the topic of self-motions of planar Stewart-Gough platforms. We discuss Duporcq's theorem from this point of view and demonstrate that it is not correct. Moreover, we also present a revised version of this theorem.

    更新日期:2019-11-01
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