Structural Synthesis of Parallel Robots via Geometric Permutation of Coupling-Joint Alignments and Leg Chains

Parallel robots present advantages over serial robots for applications that benefit from low moving masses and energy consumption, while a low ratio of workspace to installation space is tolerable. Many structures for parallel robots have been found theoretically, but only a limited part of them has been practically applied yet. To find the best robot for a given task, a database of all suitable robots has to be available to perform a combined structural and dimensional synthesis. The structural synthesis defines leg chains and determines the alignment of the legs’ coupling joints. The latter can be either seen as part of the dimensional synthesis as a variable in this otherwise continuous optimization problem or as part of the structural synthesis as a discrete property of a robot. As the robot’s end-effector degrees of freedom (DoFs) are influenced by this alignment, it is explicitly considered as part of the structural synthesis in this work. A geometric permutation gives all combinations of leg chains and alignments of base- and platform-coupling joints and assesses the resulting parallel robot’s DoFs by numeric evaluation in a dimensional synthesis. It creates a parallel-robot database that includes the degrees of freedom for symmetric, fully parallel robots with the motion patterns of three translational and zero to three rotational DoFs: 3T0R, 3T1R, 3T2R, and 3T3R. In total, 94, 61, 21, and 223 structures for the respective motion patterns were obtained, and some robots were found that had not yet been described in the literature. The proposed permutational and numeric approach presents an alternative to structural synthesis via computer algebra systems and is computationally feasible despite the high number of parallel-robot candidates. The database, published as open source, can be further used in a combined structural and dimensional synthesis to optimize all possible robots for a given task and select the best.