基于运动微分方程与加速度的刚体运动姿态算法  

Attitude Algorithm of Motion Rigid Body Based on Differential Equations and Acceleration

作　　者：张楠[1] 王智[1] 王德伦[1] ZHANG Nan;WANG Zhi;WANG De-lun(School of Mechanical Engineering,Dalian University of Technology,Liaoning Dalian 116024,China)

机构地区：[1]大连理工大学机械工程学院,辽宁大连116024

出　　处：《机械设计与制造》2021年第10期215-219,224,共6页Machinery Design & Manufacture

基　　金：国家自然科学基金资助项目(U1808213)。

摘　　要：对运动刚体上点的轨迹、速度、加速度与刚体运动姿态之间的关系进行研究,提出了一种由刚体上非共线三点的线加速度解算刚体空间姿态角的方法。利用刚体上点的运动学方程与瞬轴性质导出刚体角速度与刚体空间姿态角的关系,进而由其微分形式得到刚体上不共线三点的线加速度与刚体空间姿态之间满足的微分方程组。通过空间RCCC机构正向求解瞬轴与反向求解姿态角的方法对上述算法进行验证,结果表明,该算法可以应用于机构空间运动姿态的求解中。In this paper,the relationship between the trajectory,velocity and acceleration of a point and the motion attitude of a moving rigid body is studied.A method for calculating the space attitude angle of motion rigid body is presented based on the known linear acceleration of three non-collinear points in fixed coordinate system.By combining kinematic equation of points and the property of instantaneous screw axis(ISA),the relationship between the angular velocity and the attitude angle is obtained.Then,the nonlinear differential equations related to the linear acceleration of three non-collinear points and the attitude angle of the rigid body are established.Finally,the spatial RCCC four-bar linkage is used to verify the correctness of the algorithm by calculating the ISA for positive solution and the attitude angle for inverse solution.The result shows that the model can be used to calculate space attitude angle of mechanism.

关 键 词：刚体运动姿态 运动微分方程 加速度 空间RCCC机构 

分 类 号：TH16[机械工程—机械制造及自动化] TH112