Global Planning of Dynamically Feasible Trajectories for Three-DOF Spatial Cable-Suspended Parallel Robots
This paper addresses the dynamic trajectory planning of three-DOF spatial cable-suspended parallel robots. Based on a dynamic model of the suspended robot, a set of algebraic inequalities is obtained that represents the constraints on the cable tensions.
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Abstract This paper addresses the dynamic trajectory planning of three-DOF spatial cable-suspended parallel robots. Based on a dynamic model of the suspended robot, a set of algebraic inequalities is obtained that represents the constraints on the cable tensions. Dynamic feasibility is then established using interval arithmetics on the latter inequalities in order to obtain global conditions on the trajectory parameters that can guarantee that the cable tensions remain positive throughout the trajectory. Such conditions are obtained for a variety of parametric trajectories. When periodic functions are used in the design of the trajectories, it is shown that special frequencies arise that are akin to natural frequencies of pendulum-type systems. These special frequencies can be used in practice to greatly simplify the trajectory planning. An experimental implementation on a three-dof cable-suspended prototype is presented. As demonstrated, the proposed trajectory planning approach can be used to plan dynamic trajectories that go beyond the static workspace of the mechanism, thereby opening novel applications and possibilities for cable-suspended robots.
1 Introduction The dynamics of cable-driven parallel mechanisms has been a topic of interest since the introduction of the first designs. Indeed, cable-driven parallel mechanisms have the potential to produce very fast motions and the control of such motions requires a proper understanding of the dynamics of the mechanical system. In fully constrained cable-driven systems such as those presented in [13, 15, 22] (and many others), a dynamic model is highly relevant. In such mechanisms, very high speed motions can be generated due to the wrench closure property. C. Gosselin (B) Département de Génie Mécanique, Université Laval, 1065 Avenue de la Médecine, Québec, QC G1V 0A6, Canada e-mail: [email protected] T. Bruckmann and A. Pott (eds.), Cable-Driven Parallel Robots, Mechanisms and Machine Science 12, DOI: 10.1007/978-3-642-31988-4_1, © Springer-Verlag Berlin Heidelberg 2013
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The dynamic modelling of fully constrained cable-driven parallel mechanisms was addressed in several publications. For instance, in [5, 7, 8], and [19], dynamic models are proposed for mechanisms with more cables than degrees of freedom. One important issue in this context is the optimization of the distribution of the tensions among the cables. This issue is investigated in more detail in [4, 9] and [16]. As opposed to fully constrained cable-driven parallel mechanisms, cablesuspended mechanisms use an external force—typically gravity—to maintain their cables in tension. They are not redundantly actuated, i.e., they include at most as many actuators as degrees of freedom. Cable-suspended parallel robots have been proposed in the literature as potential candidates for applications that require very large workspaces or as mechanisms that can provide effective payload to mass ratios. One of the first cable-suspended mechanisms that was built is the Robocrane [1], developed
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