Jacobian matrix establishment for parallel-serial hybrid robots based on end-effector screw describing coordinate system

LI Wei; WANG Hui

doi:10.16578/j.issn.1004.2539.2026.06.015

Abstract：[Objective]Aiming at the problems that the screw method based on the traditional base coordinate system cannot directly map the joint drive speed to the speed of the end-effector point,and the force Jacobian matrix needs to introduce additional couple moments which reduces the calculation efficiency,a new method for establishing the Jacobian matrix of parallel-serial hybrid robots based on the end-effector screw describing coordinate system was proposed.[Methods]Firstly,the end-effector screw describing coordinate system was defined,and its core advantages in velocity and static modeling were clarified.Secondly,the general construction process of velocity and force Jacobian matrices for parallel-serial hybrid robots was derived.Then,taking the TriMule robot as the research object,the derivation model of its Jacobian matrix was established based on the screw reciprocal product theory,and the correctness of the model was verified by comparison with the traditional method.Finally,the forward position solution of the robot was solved,and the numerical example calculation and verification of the Jacobian matrix were completed with Matlab software.[Results]The results show that the Jacobian matrix established by the proposed method can directly realize the mapping from joint drive speed to the speed of the end-effector point,and its transpose is the force Jacobian matrix.Numerical examples show that the maximum relative error of the end velocity calculated by the two methods is less than 0.6%,which verifies the correctness of the method.This method has clearer physical meaning,eliminates the links of velocity conversion and additional moment calculation,and provides reference for real-time control and static analysis of hybrid robots.