Displacement Analysis of Under-Constrained Cable-Driven Parallel Robots

This dissertation studies the geometric static problem of under-constrained cable-driven parallel robots (CDPRs) supported by n cables, with n ≤ 6. The task consists of determining the overall robot configuration when a set of n variables is assigned. When variables relating to the platform posture are assigned, an inverse geometric static problem (IGP) must be solved; whereas, when cable lengths are given, a direct geometric static problem (DGP) must be considered. Both problems are challenging, as the robot continues to preserve some degrees of freedom even after n variables are assigned, with the final configuration determined by the applied forces. Hence, kinematics and statics are coupled and must be resolved simultaneously. In this dissertation, a general methodology is presented for modelling the aforementioned scenario with a set of algebraic equations. An elimination procedure is provided, aimed at solving the governing equations analytically and obtaining a least-degree univariate polynomial in the corresponding ideal for any value of n. Although an analytical procedure based on elimination is important from a mathematical point of view, providing an upper bound on the number of solutions in the complex field, it is not practical to compute these solutions as it would be very time-consuming. Thus, for the efficient computation of the solution set, a numerical procedure based on homotopy continuation is implemented. A continuation algorithm is also applied to find a set of robot parameters with the maximum number of real assembly modes for a given DGP. Finally, the end-effector pose depends on the applied load and may change due to external disturbances. An investigation into equilibrium stability is therefore performed

Analysis of the Workspace of Tendon-based Stewart Platforms

Tendon-based Stewart platforms are a concept for innovative manipulators where the load to move almost coincides with the payload. After an overview over the state of research and some concepts of kinematics (singularity and redundancy), the thesis discusses aspects of the technically usable workspace (positive tendon forces, limits of tension, singularity, stiffness, collisions between tendens). A representation of the controllablwe workspace by means of polynomial inequalities is developed. Optimal solutions are provided to the problem of finding appropriate force distributions in the tendons. These solutions can be discontinuous in time, but they can be approximated with continuous ones. An algorithm is given for this. From these results, a quality measure for workspace is derived and used to state design rules which help achieving good workspaces. For some systems, sample trajectories are simulated.</p