On-orbit servicing, active debris removal or assembling large structures on orbit are only some of the tasks that could be accomplished by space robots. In all these cases, a contact between a space robot and the satellite being serviced, deorbited, or assembled will occur. This contact results in a contact force exerted on the space robot, and therefore momenta of the space robot system are no longer

Computational prediction of 3D crutch-assisted walking patterns is a challenging problem that could be applied to study different biomechanical aspects of crutch walking in virtual subjects, to assist physiotherapists to choose the optimal crutch walking pattern for a specific subject, and to help in the design and control of exoskeletons, when crutches are needed for balance. The aim of this work

In this paper, a novel hybrid fractional-order control strategy for the PUMA-560 robot manipulator is developed and presented, which combines the derivative of Caputo–Fabrizio and the integral of Atangana–Baleanu, both in the Caputo sense. The fractional-order dynamic model of the system (FODM) is also considered which consists of two models, the robot manipulator model, and the model of the induction

We develop a referenced nodal coordinate formulation (RNCF) to study the dynamics of flexible bodies undergoing large-distance travels and/or high-speed rotations. RNCF is similar to the absolute nodal coordinate formulation (ANCF) but is presented in a noninertia reference coordinate system (RCS). The position vector and rotation matrix of the RCS describe translational and rotational motions of the

The aim of this paper is to discuss the effect of cosimulation on a railway vehicle/track/soil model. Firstly, only the vehicle and a flexible track are considered without taking the soil flexibility into account. Two well-known co-simulation approaches are used: a parallel approach, called Jacobi, and a sequential approach, called Gauß–Seidel. The definition of the subsystems, thus the place at which

Using detailed musculoskeletal models in computer simulations of human movement can provide insights into individual muscle and joint loading; however, these muscle models increase problem dimensionality and require difficult-to-fit parameters. Here, we provide a brief overview of a muscle model alternative, muscle torque generators (MTGs), and highlight how MTG functions have been used by researchers

In this study, we develop an analytical formula to approximate the damping coefficient as a function of the coefficient of restitution for a class of continuous contact models. The contact force is generated by a logical point-to-point force element consisting of a linear damper connected in parallel to a spring with Hertz force–penetration characteristic, while the exponent of deformation of the Hertz

Traditional physics-based contact models have been widely used for describing various contact phenomena such as robotic grasping and assembly. However, difficulties in carrying out contact parameter identification as well as the relatively low measurement accuracy due to complex contact geometry and surface uncertainties are the limiting factors of the physics-based contact modeling methods. In this

We discuss modeling, algorithmic, and software aspects that allow a simulation tool called Chrono::Granular to run billion-degree-of-freedom dynamics problems on commodity hardware, i.e., a workstation with one GPU. The ability to scale the solution to large problem sizes is traced back to an adimensionalization process combined with the use of mixed-precision data types that reduce memory pressure

The superellipsoids, part of the family of superquadratics, have geometric and mathematical properties that not only make them suitable for the representation of solids, ranging from spheres to relatively thin sheets, but also allow describing a very broad number of complex geometries. Their mathematical description favors a very efficient numerical treatment, in particular when used in the context

Collision between hard objects causes abrupt changes in the velocities of the system, which are characterized by very large contact forces over very small time durations. A common approach in the analysis of such collisions is to describe the system velocities using an impulse–momentum based relationship. The time duration of impact and the deformations at the contact points are usually assumed to

The dynamic response of many flexible multibody systems of practical interest is periodic. The investigation of such problems involves two intertwined tasks: first, the determination of the periodic response of the system and second, the analysis of the stability of this periodic solution. Starting from Hamilton’s principle, a unified solution procedure for continuous and discontinuous Galerkin methods

An optimization-based multibody dynamics modeling method is proposed for two-dimensional (2D) team lifting prediction. The box itself is modeled as a floating-base rigid body in Denavit–Hartenberg representation. The interactions between humans and box are modeled as a set of grasping forces which are treated as unknowns (design variables) in the optimization formulation. An inverse-dynamics-based

A review of the current use of multibody dynamics methods in the analysis of the dynamics of vehicles is given. Railway vehicle dynamics as well as road vehicle dynamics are considered, where for the latter the dynamics of cars and trucks and the dynamics of single-track vehicles, in particular motorcycles and bicycles, are reviewed. Commonalities and differences are shown, and open questions and challenges

Foot–ground contact models play an important role in the accuracy of predictive human gait simulations, and there is a need for a computationally-efficient dynamic contact model for predictive and evaluative studies. In this research, we generated symbolic dynamic equations for a 2D torque-driven 11-DOF human model with a 3D ellipsoidal volumetric foot–ground contact model. The main goal was to increase

Sit-to-stand (STS) motion is one of the most important tasks in daily life and is one of the key determinants of functional independence, especially for the senior people. The STS motion has been extensively studied in the literature, mostly through experiments. Compared to numerous experimental studies, there are limited simulations with mostly assuming bilateral symmetry for STS tasks. However, it

This paper presents a general explicit differential form of Lagrange’s equations for systems with hybrid coordinates and general holonomic and nonholonomic constraints. The appropriate constraint conditions are imposed on d’Alembert–Lagrange principle via Lagrange multipliers to find the correct equations of state of nonholonomic systems. The developed equations take the differential form in terms

Much of the previous research on modeling and simulation of cycling has focused on seated pedaling, modeling the crank load with an effective resistive torque and inertia. This study focuses on modeling standing starts, a component of certain track cycling events in which the cyclist starts from rest and attempts to accelerate to top speed as quickly as possible. A ten degree-of-freedom, two-legged

The conventional use of inverse dynamics applied to gait analysis involves the estimation of joint forces and moments based on kinematic data, anthropometric parameters and force plate data. The procedure uses the measured ground reactions and, beginning with those segments in contact with the ground, calculates joint forces and moments at each successive segment. However, this procedure cannot always

Forward dynamics golf swing simulations are important to gain insight into how a golfer should swing a particular club and which design improvements should be considered by golf club manufacturers. A new method of optimizing a four degree-of-freedom (DoF) biomechanical golfer model swinging a flexible shaft with a rigid clubhead was developed using a direct orthogonal collocation approach. The kinematic

New products in the automotive and aerospace industries must provide increased energy efficiency and exceed previous performance, safety and reliability. To meet these expectations, the role of simulation continues to grow. Within this context, simulation models are used in real-time embedded applications such as advanced real-time control and virtual sensing. Both applications require the execution

This paper addresses the modeling and simulation of a homogeneous disk that undergoes plane motion constrained to be in permanent contact with and in the same plane as a two-dimensional curve described by a parametric equation. Except for the elementary cases in which the curve is a straight line or an arc of circumference, the investigated problem presents significant challenges to both modeling and

This paper describes the development of a dynamic model for parallel manipulators based on the Lagrange–D’Alembert equation, the Hessian matrix of the kinetic energy of the manipulator, and the Jacobian/Hessian matrices of the constraint equations. The model generates the forward and inverse dynamics formulations of parallel manipulators. First, the kinematic relations between the input actuated variables

This paper describes a new numerical procedure for the modelling and simulation of the wheel–rail contact in railway dynamic simulations. The method is called knife-edge-equivalent contact constraint method, or simply KEC-method. Using this method, the wheel–rail contact is modelled as rigid or constraint-based using a set of kinematic constraints that eliminates one-degree of freedom of relative wheel–rail

A collision between two bodies is a usual phenomenon in many engineering applications. The most important problem with the collision analysis is determining the hysteresis damping factor or the hysteresis damping ratio. The hysteresis damping ratio is related to the coefficient of restitution. In this paper, an explicit expression is determined for this relation. For this reason, a parametric expression

In this paper, a novel dynamic model of coupling translation joints with subsidence for time-varying load in a planar mechanical system is established. One translational joint has four working scenarios, which are free motion, one corner rub-impact, two adjacent corners rub-impact and two opposite corners rub-impact. However, the rub-impact of double coupling translation joints are not a simple superposition

The dynamic modeling for the foldable origami space membrane structure considering contact-impact during the deployment is studied in this paper. The membrane is discretized using the triangular elements of the Absolute Nodal Coordinate Formulation (ANCF), and the stress–strain relationship of the membrane is determined based on the Stiffness Reduction Model (SRM). A mixed method is proposed for the

This paper proposes a systematic methodology to obtain a closed-form formulation for dynamics analysis of a new design of a fully spherical robot that is called a 3(RSS)-S parallel manipulator with real co-axial actuated shafts. The proposed robot can completely rotate about a vertical axis and can be used in celestial orientation and rehabilitation applications. After describing the robot and its

In this paper, the contact control problem of a space robot to grasp a non-cooperative satellite is investigated in detail, and a new capture control strategy is proposed. Firstly, the dynamic equation of the robot system is derived based on the multibody dynamics theory, and a modified Hertz model is used to describe the contact force between the robot end-effector and the target satellite. Then,

Skeletal muscles usually wrap over multiple anatomical features, and their mass moves along the curved muscle paths during human locomotion. However, existing musculoskeletal models simply lump the mass of muscles to the nearby body segments without considering the effect of mass flow, which has been shown to induce non-negligible errors. A mass-variable multibody formulation is proposed here to simultaneously

It has been known that bicycle stability is closely linked to a pair of ordinary differential equations (ODEs). The linearization technique used to derive these ODEs, nevertheless, has yet to be thoroughly examined. For this purpose, we conduct an analysis of the dynamics of the Whipple bicycle, starting with the contact kinematics, using the Gibbs–Appell method. The effort results in a complete nonlinear

The use of principal points and principal vectors in the formulation of the equations of motion of a general 4R planar four-bar linkage is shown with two kinds of methods, one that opens kinematic loops and one that does not. The opened kinematic loop approach analyses the moving links as a system with a tree connectivity, introducing reaction forces for closing the loops. Compared with the conventional

A novel formulation for the description of spatial rigid body motion using six non-redundant, homogeneous local velocity coordinates is presented. In contrast to common practice, the formulation proposed here does not distinguish between a translational and rotational motion in the sense that only translational velocity coordinates are used to describe the spatial motion of a rigid body. We obtain

Abstract The dynamic characteristics of thin-walled four-point contact ball bearing with crown-type cage are important to the dynamic performance and motion accuracy of an industrial robot. Considering multi-clearances, dynamic contact and impact relationships of the ball, ring raceway and crown-type cage, a general methodology for dynamic simulation analysis of the bearing is investigated in the proposed

Abstract This paper develops a compact form dynamics controller to generate multi-compliant behaviors for a new designed tetrapod-on-wheel robot with one manipulator. The whole-body compliant torque controller is stated through one null-space-based convex optimization and compatible null-space-based impedance controllers. Different from fixed contact points of conventional quadruped robots, the kinematic

Abstract Sensitivity analysis computes the derivatives of general cost functions that depend on the system solution with respect to parameters or initial conditions. This work develops adjoint sensitivity analysis for hybrid multibody dynamic systems. The adjoint sensitivity is commonly referred to as backward propagation. Hybrid systems are characterized by trajectories that are piecewise continuous

Abstract The simulation of mechanical devices using multibody system dynamics (MBS) algorithms frequently requires the consideration of their interaction with components of a different physical nature, such as electronics, hydraulics, or thermodynamics. An increasingly popular way to perform this task is through co-simulation, that is, assigning a tailored formulation and solver to each subsystem in

Abstract In this article we analyze the following problem: given a mechanical system subject to (possibly redundant) bilateral and unilateral constraints with set-valued Coulomb’s friction, provide conditions such that the state, which consists of all contacts sticking in both tangential and normal directions, is solvable. The analysis uses complementarity problems, variational inequalities, and linear

Abstract A unifying slipping and sticking frictional impact model for multibody systems in contact with a frictional surface is presented. It is shown that the model can lead to energetic consistency in both slip and stick states upon imposing specific constraints on the coefficient of friction (CoF) and the coefficient of restitution (CoR). A discriminator in the form of a quadratic function of the

Abstract Friction phenomena exist in almost every mechanical device. Due to its complicated nature and influence on the system performance, extensive dynamic simulations are often required in the early system design stage. In this work, a novel approach for eliminating the numerical discontinuity in the classical Coulomb law and its extension is developed. Specifically, the method improves the computation

Abstract The computational procedures of higher-order implicit integrators for mechanical systems with friction are provided in this paper. The dynamic equations are established using the augmented Lagrangian formulation, and set-valued friction forces are described by projection functions. To reduce the accuracy loss caused by event transitions and to eliminate spurious oscillations in the acceleration

Abstract The aim of this work is the development of a robust and accurate time integrator for the simulation of the dynamics of multibody systems composed of rigid and/or flexible bodies subject to frictionless contacts and impacts. The integrator is built upon a previously developed nonsmooth generalized-\(\alpha \) scheme time integrator which was able to deal well with nonsmooth dynamical problems

Abstract This work presents a contribution to the active image stabilization of optical systems, involving model development, control design, and the hardware setup. A laboratory experiment is built, which demonstrates the vibration sensitivity of a mechanical-optical system. In order to stabilize the undesired image motion actively, a model-based compensation of the image vibration is developed, realized

Abstract The isotropic compliance property is examined in the Special Euclidean Group SE(3) in the case of redundant manipulators. The redundancy problem is solved by means of the QR decomposition of the transposed Jacobian matrix, and the compliance property is achieved by means of active stiffness regulation. Thanks to the defined control matrices, the control system realizes the isotropy condition

Existing Floating Offshore Wind Turbine (FOWT) platforms are usually designed using static or rigid-body models for the concept stage and, subsequently, sophisticated integrated aero-hydro-servo-elastic models, applicable for design certification. For the new technology of FOWTs, a comprehensive understanding of the system dynamics at the concept phase is crucial to save costs in later design phases

Multibody models are often coupled with other domains in order to enlarge the scope of computer-based analysis. In particular, modeling multibody systems (MBSs) in interaction with granular media is of great interest for industrial process such as railway track maintenance, handling of aggregates, etc. This paper presents a strong coupling methodology for unifying a multibody formalism using relative

In multibody systems, there are not only holonomic bilateral constraints, but also unilateral constraints. The existence of unilateral constraints brings nonsmooth contact dynamic problems into multibody dynamic systems. In this paper, we present an approach based on the symplectic method and the linear complementary method to solve multibody dynamic problems with impact contact. As the symplectic

Joints with clearances in flexible multibody systems have been investigated for many years. However, the previous work is mainly concerned with the lower pair joints with small clearances. The aim of this paper is to present a formulation for the sliding joint with clearance between a flexible beam and a rigid hole, with special focus on the frictional contact. We thoroughly discuss a contact detection

The Floating Frame of Reference Formulation (FFRF) is one of the most widely used methods to analyze flexible multibody systems subjected to large rigid-body motion but small strains and deformations. The FFRF is conventionally derived via a continuum mechanics approach. This tedious and circuitous approach, which still attracts attention among researchers, yields so-called inertia shape integrals

The adjoint method shows an efficient way to incorporate inverse dynamics to engineering multibody applications, as, e.g., parameter identification. In case of the identification of parameters in oscillating multibody systems, a combination of Fourier analysis and the adjoint method is an obvious and promising approach. The present paper shows the adjoint method including adjoint Fourier coefficients

The adjoint method is an elegant approach for the computation of the gradient of a cost function to identify a set of parameters. An additional set of differential equations has to be solved to compute the adjoint variables, which are further used for the gradient computation. However, the accuracy of the numerical solution of the adjoint differential equation has a great impact on the gradient. Hence

We present a method for optimizing inputs of multibody systems for a subsequently performed parameter identification. Herein, optimality with respect to identifiability is attained by maximizing the information content in measurements described by the Fisher information matrix. For solving the resulting optimization problem, the adjoint system of the sensitivity differential equation system is employed

The real-time estimation of muscle forces could be a very valuable tool for rehabilitation. By seeing how much muscle force is being produced during rehabilitation, therapists know whether they are working within safe limits in their therapies and patients know if they are producing enough force to expect improvement. This is especially true for rehabilitation of Achilles tendon ruptures where, out

This second, of a two part paper, uses concepts from graph theory to obtain a deeper understanding of the mathematical foundations of multibody dynamics. The first part [7] established the block-weighted adjacency (BWA) matrix structure of spatial operators associated with serial and tree topology multibody system dynamics, and introduced the notions of spatial kernel operators (SKO) and spatial propagation

This is the first part of two papers that use concepts from graph theory to obtain a deeper understanding of the mathematical foundations of multibody dynamics. The key contribution is the development of a unifying framework that shows that key analytical results and computational algorithms in multibody dynamics are a direct consequence of structural properties and require minimal assumptions about

This paper presents an efficient optimal control and recursive dynamics-based computer animation system for simulating and controlling the motion of articulated figures. A quasi-Newton nonlinear programming technique (super-linear convergence) is implemented to solve minimum torque-based human motion-planning problems. The explicit analytical gradients needed in the dynamics are derived using a matrix

This paper presents an efficient dynamics-based computer animation system for simulating and controlling the motion of articulated figures. A non-trivial extension of Featherstone's O(n) recursive forward dynamics algorithm is derived which allows enforcing one or more constraints on the animated figures. We demonstrate how the constraint force evaluation algorithm we have developed makes it possible

In this work a new formulation for flexible multibody systems is presented based on the floating frame formulation. In this method, the absolute interface coordinates are used as degrees of freedom. To this end, a coordinate transformation is established from the absolute floating frame coordinates and the local interface coordinates to the absolute interface coordinates. This is done by assuming linear

This paper presents a novel model order reduction technique for 3D flexible multibody systems featuring nonlinear elastic behavior. We adopt the mean-axis floating frame approach in combination with an enhanced Rubin substructuring technique for the construction of the reduction basis. The standard Rubin reduction basis is augmented with the modal derivatives of both free-interface vibration modes

Computational speed and stability are two important aspects in the dynamics analysis of large-scale complex multibody systems. In order to improve both in the context of the multibody system transfer matrix method, a new version of the Riccati transfer matrix method is presented. Based on the new version of the general transfer matrix method for multibody system simulation, recursive formulae are developed