Solving the Direct Geometrico-Static Problem of 3-3 Cable-Driven Parallel Robots by Interval Analysis: Preliminary Resul
This paper studies the direct geometrico-static analysis of under- constrained cable-driven parallel robots with 3 cables. The task consists in finding all equilibrium configurations of the end-effector when the cable lengths are assigned. An interval-ana
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Abstract This paper studies the direct geometrico-static analysis of underconstrained cable-driven parallel robots with 3 cables. The task consists in finding all equilibrium configurations of the end-effector when the cable lengths are assigned. An interval-analysis-based procedure is proposed to numerically find the real solutions of the problem for a robot of generic geometry. Three equation sets obtained by different approaches are implemented in the problem-solving algorithm and a comparison between the main merits and drawbacks of each one of them is reported.
1 Introduction Cable-driven parallel robots (CDPRs) employ cables in place of rigid-body extensible legs in order to control the end-effector pose. CDPRs strengthen classic advantages characterizing closed-chain architectures versus serial ones, like reduced mass and inertia, a larger payload to robot weight ratio, high dynamic performances, etc., while providing peculiar advantages, such as a larger workspace, reduced manufacturing and maintenance costs, ease of assembly and disassembly, high transportability, and superior modularity and reconfigurability.
A. Berti (B) · M. Carricato Department of Mechanical Engineering (DIEM), University of Bologna, Bologna, Italy e-mail: [email protected] M. Carricato e-mail: [email protected] J.-P. Merlet COPRIN Project, French National Institute for Research in Computer Science and Control (INRIA), Sophia-Antipolis, France 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_16, © Springer-Verlag Berlin Heidelberg 2013
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A CDPR is fully-constrained if the pose of the end-effector is completely determined when actuators are locked and, thus, all cable lengths are assigned. A CDPR is, instead, under-constrained if the end-effector preserves some degrees of freedom (dofs) once actuators are locked [2, 16]. This occurs either when the end-effector is controlled by a number of cables n smaller than the number of dofs that it possesses with respect to the base or when some cables become slack in a fully-constrained robot. The use of CDPRs with a limited number of cables is justified in several applications (such as, for instance, rescue, service or rehabilitation operations [14, 18, 19]), in which the task to be performed requires a limited number of controlled freedoms (only n dofs may be governed by n cables) or a limitation of dexterity is acceptable in order to decrease complexity, cost, set-up time, likelihood of cable interference, etc. Furthermore, a theoretically fully-constrained CDPR may operate, in appreciable parts of its geometric workspace, as an under-constrained robot, namely when a full restraint of the end-effector may not be achieved because it would require a negative tension in one or more cables. Even though the above considerations motivate a careful study of under-constrained CDPRs, little research was conducted on them [1–7, 10, 15, 2
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