Reconfiguration of planar quadrilateral linkages utilizing the tensegrity principle
Introduction
Although the use of multi-axis guides with several independent actuators enables great potential and variety with regard to the required trajectories, linkages are still relevant for current applications. Due to their geometric constraints, those mechanisms feature an immense accuracy and repeatability of the kinematic behavior, e.g. the transmission ratio. However, conventional linkages are optimized for only one specific task. Thus, in order to enable adaptability respective to varying demands on the kinematics, the consideration of reconfigurable mechanisms is a promising approach. Those mechanisms enable various operation modes differing in the corresponding mechanical properties. A change between those modes, the so-called reconfiguration, allows modifying the kinematics of the mechanism. Reconfigurable mechanisms were introduced in the middle 1990s. Subsequent pioneering works show the great benefit of this kind of mechanism that this research topic gained attention. Thus, numerous approaches were developed, e.g. kinematotropic linkages [1], [2], [3], [4], metamorphic mechanisms [5], [6], [7], [8], [9], mechanisms with variable chains [10], [11], [12]. An overview and a classification of reconfigurable mechanisms are given in Kuo et al. [13], Aimedee et al. [14]. Recently, the investigation of prestressed mechanisms that enable stable equilibrium configurations is focused by researchers. For example, cable-driven mechanisms represent a gaining research topic. A variation of the prestress state of the mechanisms allows influencing the mechanical properties, like the working space, the equilibrium configuration, and the structural dynamics [15], [16], [17]. In this context, the consideration of tensegrity-based mechanisms also seems to be a promising approach. Originally, such mechanisms were established in the fields of architecture and sculpturing [18], [19]. However, tensegrity structures enable several advantages (e.g. great shape change capability, shock resistance, etc.) which also allows their application in mechanism technology. Various approaches to reconfigurable mechanisms using tensegrity structures are given in Boehler et al. [20], 21], Böhm et al. [22], Sumi et al. [23], Arsenault [24], Fasquelle et al. [25]. Moreover, multistable tensegrity structures feature several stable equilibrium configurations [26], [27]. Changing between these stable states allows reconfiguration of the structure and its kinematics. In [28] a reconfigurable linkage based on a tensegrity-based mechanism is presented.
Based on the result of [28] further investigations of a reconfigurable tensegrity-based linkage are presented in this work. In order to verify the theoretical approaches a prototype of the tensegrity-based mechanism is developed and experiments are evaluated. In chapter 2 the realization of the reconfigurable linkage due to applying the tensegrity principle is explained. The corresponding equations of motion are derived using the Lagrange formalism. The equilibrium configurations and the mechanical properties of the mechanism are evaluated in chapter 3. Furthermore, the reconfiguration of the mechanism is considered for an exemplary actuation strategy. In chapter 4, a prototype of the tensegrity-based mechanism is presented and experiments regarding the kinematics and the reconfiguration are evaluated compared to the theoretical results. In chapter 5 the results are concluded and an outlook for further research is given.
Section snippets
Reconfigurable tensegrity-based mechanism
In this chapter, conventional planar four-bar linkages are investigated. The results show two different working spaces. However, a controllable change between these operation modes is not possible due to geometric constraints. Therefore, nonholonomic constraints realized by ropes, which cannot resist compression, are implemented. This approach requires an appropriate prestress state of the mechanism to guarantee tension within the ropes during operation. This fact encourages the design of
Parameter selection
To realize a reconfiguration of the linkage appropriate mechanical parameters of the structural members have to be selected. The tensegrity-based mechanism must enable two stable equilibrium configurations corresponding to the parallel linkage and the antiparallel linkage. Moreover, the rope must be loaded by tension in those configurations. Therefore, the nonlinear system of equations shown in (8) is evaluated numerically applying the Newton-Raphson method in preliminary simulations for
Prototype of the mechanism
For the experimental verification of the theoretical approach, a prototype of the discussed tensegrity-based mechanism was developed (see Fig. 9). Therefore, the two-dimensional topology of the linkage was extended to a three-dimensional construction as suggested in Böhm [27]. The compressed members of the mechanism () are realized by struts made of aluminum and the tensioned members () are realized by standard tension springs. Member 3 which is modeled as a rope is realized
Conclusion
In this work a novel approach to realize reconfigurable mechanisms based on the tensegrity principle is presented. Conventional quadrilateral planar linkages are considered. Such mechanisms feature a great accuracy regarding the kinematics due to their geometric constraints. Moreover, these linkages enable two operation modes differing in the kinematic properties. However, a controllable change between these states is not possible due to the mentioned geometric constraints.
In this work, these
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This work is supported by Deutsche Forschungsgemeinschaft (DFG) within the SPP 2100 - projects ZE714/14-1, BO4114/3-1.
References (35)
- et al.
A new family of reconfigurable parallel mechanisms with diamond kinematotropic chain
Mech. Mach. Theory
(2014) - et al.
Design of general kinematotropic mechanisms
Robot. Comput. Integr. Manuf.
(2016) - et al.
Design and analysis of a metamorphic mechanism cell for multistage orderly deployable/retractable mechanism
Mech. Mach. Theory
(2017) - et al.
Method for configuration synthesis of metamorphic mechanisms based on functional analyses
Mech. Mach. Theory
(2018) - et al.
Configuration synthesis of mechanisms with variable topologies
Mech. Mach. Theory
(2009) - et al.
Type synthesis and reconfiguration analysis of a class of variable-DOF single-loop mechanisms
Mech. Mach. Theory
(2015) - et al.
Systematization of morphing in reconfigurable mechanisms
Mech. Mach. Theory
(2016) - et al.
Discrete reconfiguration planning for cable-driven parallel robots
Mech. Mach. Theory
(2016) - et al.
From modeling to control of a variable stiffness device based on a cable-driven tensegrity mechanism
Mech. Mach. Theory
(2017) - et al.
Compliant multistable tensegrity structures
Mech. Mach. Theory
(2017)