Workspace optimization of 3-legged UPU and UPS parallel platforms with joint constraints

In this paper the work-space optimization of 3-legged translational UPU and orientational UPS parallel platforms under joint constraints is performed. The workspace of both platforms is parametrized using several design parameters that span a large range of values. In this paper both the unconstrained and the constrained workspaces (i.e., workspace with joint limits) arc used. For the workspace of each design configuration three performance indices are calculated using a Monte Carlo method: a) the workspace volume; b) the average of the inverse of the condition number and c) a Global Condition Index which is a combination of the other indices. Plots of each performance index as a function of the design parameters are generated and optimal values for these design parameters are determined. For the optimal design, it is shown that by introducing joint limits, the global isotropy of the parallel platforms is improved at the cost of workspace reduction.