A Coupled Spherical Rehabilitation Linkage Synthesis Method Based On SU(2) Matrix And Fourier Transform

Mechanism synthesis is a discipline that studies how to design mechanisms to achieve a given trajectory or motion and is the focus of research in the field of mechanism science.In engineering applications,many scenes need machines that can realize complex spatial trajectories and spatial motion,such as rehabilitation robots.As a kind of single-degree-offreedom mechanism that can realize complex spatial motion,coupled spherical linkage has a broad application prospect because of its large workspace and non-interference characteristics while meeting such requirements.In order to study the coupled spherical linkage,this paper proposes using the SU(2)matrix(special unitary matrix of degree 2)on the kinematics analysis and modelling.So,the general expression of the end trajectory and motion of the coupled spherical linkage is obtained.Then using the derived kinematics model and Fourier transform theory,the problems of path synthesis and motion synthesis are emphatically solved,which enriches and develops the theory of mechanism analysis and synthesis.This paper mainly carries out the following three aspects of work:(1)The relation between SU(2)matrix and the motion of spherical rigid body is expounded.Then a general method of representing the output trajectory and motion of the spherical coupling linkage mechanism by SU(2)matrix is presented.Therefore,the kinematics models of the mechanism design parameters,such as link size,fixed pivot position and transmission ratio,were derived and established.Last,Fourier descriptors are used to derive the Fourier descriptor equations of trajectories and motions.(2)To solve the problem of path synthesis and motion synthesis of coupled spherical linkages,an efficient trajectory synthesis algorithm and motion synthesis algorithm are proposed based on Fourier transform theory.These algorithms simplify the comparison of high-dimensional data to low-dimensional data,so the dimensional design parameters satisfying the least square error condition can be obtained quickly.(3)A general design method of a novel single-degree-of-freedom upper limb rehabilitation robot was proposed,and a single-degree-of-freedom upper limb rehabilitation robot mechanism was constructed by using the dimensional synthesis algorithm of coupled spherical linkages.At the same time,the design process of the upper limb rehabilitation robot based on a group of user data was taken as an example to verify the practicability of the general design method and the engineering feasibility of the coupled spherical linkage synthesis theory.