Inverse and Forward Force Transmission Analyses of Parallel Manipulators using Dimensionally Homogeneous Jacobian Matrices

유니트 일치된 자코비안 행렬을 이용한 병렬구조 로봇의 힘전달 해석

In order to avoid the unit inconsistency problem in the conventional Jacobian matrix, previously we presented new formulation of a dimensionally homogeneous inverse Jacobian matrix for parallel manipulators with a planar mobile platform by using three end-effector points based on the velocity relationship [1]. This paper presents force relationships between joint forces and Cartesian forces at the three End-Effector points. The derived force relationships can then be used for analyses of the input/output force transmission. These analyses, forward and inverse force transmission analyses, depend on the singular values of the derived dimensionally homogeneous Jacobian matrix. Using the proposed force relationship, a numerical example is presented for actuator size design of a 3-RRR planar parallel manipulator.