Optimal Kinematic Design of Spatial Parallel Manipulators: Application to Linear Delta Robot

Abstract

An optimal kinematic design method suited for parallel manipulators is developed. The kinematic optimization process yields a design that delivers the best compromise between manipulability and a new performance index, space utilization. It is shown that the exhaustive search minimization algorithm is effective for as many as four independent design variables and presents a viable alternative to advanced nonlinear programming methods. The proposed kinematic optimization method is applied to the Linear Delta: a three degree of freedom translational manipulator. The kinematics of the Linear Delta are solved via the polynomial method. The mobility, workspace and manipulability characteristics are examined. It is shown that the Linear Delta’s manipulability generally exhibits relatively little variation when compared to space utilization. The tendency exists for the solution to converge on a zero workspace size architecture when manipulability is optimized alone. The inclusion of the space utilization index in the cost function is crucial for obtaining realistic design candidates.