新型3-PRRS并联机构的位置正反解分析  

Forward and Inverse Position Kinematics Analysis of a New 3-PRRS Parallel Mechanism

作　　者：郭宗和[1] 杜晴晴 杨启志[2] 

机构地区：[1]山东理工大学,淄博255049 [2]江苏大学,镇江212013

出　　处：《中国机械工程》2015年第4期451-455,463,共6页China Mechanical Engineering

基　　金：国家自然科学基金资助项目(50905077);山东省自然科学基金资助项目(ZR2012EEL05)

摘　　要：对新型六自由度3-PRRS并联机构进行运动学分析,推导了解析形式的运动学反解,利用封闭解法研究其运动学全部正解。根据每条支链2个转动副对动平台的不同影响,通过坐标变换和引入角度变量φi,得到动平台3个铰链点坐标;以这三点之间的固定长度为约束条件,建立约束方程,得到以φi为变量的3个超越方程,通过消元法得到16次线性代数方程;利用MATLAB软件编程求解全部位置正解。应用算例对位置正反解进行了数值验证,正解结果与反解结果吻合。研究结果为应用于虚拟轴并联机床的新型3-PRRS并联机构的尺度综合、奇异位形分析、输出误差分析和轨迹控制等方面的研究奠定了基础。Kinematics based on a new 6-DOF 3-PRRS parallel mechanism were studied,the analytical form of inverse kinematics was got and closed analytic method was used to study all the forward position solutions.According to the effects of two different revolute pairs on the moving platform,coordinate transformation was used and the angle variablesφi were introduced to obtain the coordinates of three points on the moving platform.And the constant length between the three points on the moving platform was regarded as the restrict condition to obtain the constrained equations.Then three transcendental equations withφias variables were obtained,and 16 times linear algebraic equation was obtained by elimination method.MATLAB software was used to solve all the forward position solutions.Finally,a numerical example was used to verify the validity of the theories and conclusions.Thus the foundation for dimensional synthesis,singularity analysis,output error analysis and trajectory control of the new 3-PRRS parallel mechanism applied on the virtual-axis hexapod machine was laid.

关 键 词：并联机构 封闭解法 位置正反解 六自由度 

分 类 号：TH112[机械工程—机械设计及理论]