具有弧形移动副的3-RPS并联机构刚度特性分析

Stiffness Characteristics Analysis of 3-RPS Parallel Mechanism With Arc Prismatic Pairs

提出了1种具有弧型移动副的3-RPS并联机构,该机构由定平台、动平台和三条支链组成。每个分支运动链包括1个转动副R,1个弧形移动副P和1个球铰S。其中,3个转动副R的轴线共面,并彼此成60°相交。运用螺旋理论对该机构的自由度进行了分析。该并联机构动平台具有3个转动自由度,并且动平台的转动中心是各支链球铰中心与弧形连杆中心连线的交点,此交点随动平台的位姿变化而变化;另外,通过机构各个分支的螺旋互易积,获得机构的约束雅克比矩阵、驱动雅克比矩阵和全雅克比矩阵;并根据守恒协调刚度矩阵,求出机构的结构位形刚度以及外力作用影响产生的刚度,为后续的研究其动力学、运动学性质奠定了基础。

The 3-RPS parallel mechanism with arc prismatic pairs was proposed,this mechanism possesses a moving platform,a fixed platform,and three limb kinematic chain. The limb kinematic chain consists of revolute pair R,a prismatic pair P,and a spherical joint S. The axis of revolute pairs are intersect each other and coplanar,the angle between two axis is 60°. Mobility of mechanism was analyzed via screw theory. This mechanism with three degrees of freedom,and the rotational center of moving platform is intersection point that passing through each center of arc of arc rods and the center of spherical joints,the intersection point changes with the posture of the moving platform.Furthermore,each limb kinematic chain was analyzed by reciprocal basis screw,the Jacobian constraint matrix,the Jacobian actuation matrix and the Jacobian overall matrix are obtained. Then the stiffness of structural configuration and the stiffness caused by an external force were derived based on the conservative congruence transformation（ CCT）stiffness matrix. The result provides a theoretical basis for kinematics and dynamics of the mechanism.