Reconfiguration of planar quadrilateral linkages utilizing the tensegrity principle

https://doi.org/10.1016/j.mechmachtheory.2020.104172Get rights and content

Highlights

  • Reconfiguration of conventional linkages by applying one-sided limited nonholonomic constraints.

  • Mechanical modeling of tensegrity-based mechanism using the Lagrange formalism.

  • Numerical simulation of equilibrium configurations/stiffness/kinematics/reconfiguration.

  • Development of a prototype of a reconfigurable tensegrity-based mechanism.

  • Experimental investigation of equilibrium configurations/stiffness/kinematics/reconfiguration.

Abstract

The development of reconfigurable planar four-bar linkages by applying the tensegrity principle is considered. Conventional quadrilateral linkages enable two operation modes differing in the kinematic behavior. However, a change between these states is not possible due to the geometric constraints. To enable a reconfiguration between the different modes one-sided limited nonholonomic constraints are introduced in this work. This issue is realized by applying ropes that cannot resist compression. However, to guarantee an appropriate load case in operation a prestress within the mechanism is required. Hence, the linkage is extended to a tensegrity-based mechanism. The structural dynamics are derived using the Lagrange formalism and the structural behavior is evaluated using numerical simulations. Furthermore, a prototype of an exemplary tensegrity-based mechanism is manufactured and experiments regarding the mechanical properties, in particular the reconfiguration, are performed. The results suggest the potential benefit of applying the tensegrity principle within conventional planar four-bar linkages.

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 (j=1,2,4,5) are realized by struts made of aluminum and the tensioned members (j=6,7,8,9) 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.

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