Transmission Angle Analysis of a Type of Parallel Manipulators

Abstract

In most research works, the conditioning index is used to analyze the kinematic performance of a type of parallel manipulators whose traveling plate has only translation in the workspace, and each limb is made up of three joints and two moving links. However, it is difficult to determine the reasonable limit value of the conditioning index as the design criterion. Therefore, this paper defines two types of transmission angles to evaluate the kinematic performance of parallel manipulators, with which the direct and indirect singularities can be identified in a straightforward manner. Taking both the Diamond and Delta parallel manipulators as examples, the relationships are investigated between the angles and the condition number of the Jacobian, which is a vital performance index for parallel manipulators throughout the workspace. Then, simulation studies are conducted to prove the effectiveness of two kinds of transmission angles for the Diamond and Delta robots. It indicates that the defined angles are well characterized compared with the condition number of the Jacobian matrix in evaluating the kinematic performance of the parallel manipulators and determining the workspace.