南京理工大学学报（自然科学版）2026，Vol.50Issue(1)：22-30,9.DOI:10.14177/j.cnki.32-1397n.2026.50.01.003
多体系统中邻接体相对运动显式约束方程的普遍形式
A general form of explicit constraint equations for the relative motion of joints in a multibody system
摘要
Abstract
The key to recursive kinematics of a multibody system is to study the relative motion between two adjacent bodies constrained by a joint.In this work,vectors and finite rotation tensors are used to describe the translation and rotation of rigid bodies with general spatial motion,respectively.Starting from the basic kinematics of rigid bodies and through rigorous deduction,the theorem of explicit joint constraint equation(EJCE)is proposed:the difference between the spatial acceleration twists of the outboard and inboard joint coordinate systems is a linear function of the second-order time derivatives of the joint coordinates,where the Jacobian matrix is a function of time and joint coordinates,and the inhomogeneous bias term is a function of time,joint coordinates and their first-order time derivatives.This theorem does not rely on the specific types of joints,and is independent of the choice of joint coordinate systems as well as joint coordinates,and is thus universal.Further,a calculation method for the Jacobian matrix in the EJCE is presented,which does not depend on the specific type of a joint and the selection of rotation parameters of the joint coordinates.In a final example,a spherical joint that constrains two adjacent bodies is illustrated.The Jacobian matrix in the EJCE is obtained using both the proposed method and the Euler's kinematic equations.The results are consistent,which validates the proposed method.This paper clarifies the existence of the general form of the EJCE and the computability of its Jacobian matrix,which is of theoretical significance for the recursive kinematics of multibody systems.关键词
铰/显式约束方程/有限转动张量/方向余弦矩阵/递归运动学Key words
joint/explicit constraint equation/finite rotation tensor/direction cosine matrix/recursive kinematics分类
数理科学引用本文复制引用
周秦渤,王景弘..多体系统中邻接体相对运动显式约束方程的普遍形式[J].南京理工大学学报（自然科学版）,2026,50(1):22-30,9.基金项目
国家自然科学基金(12302049) （12302049）
中央高校基本科研业务费专项资金(30924010820) （30924010820）
