Analysis of Two Spherical Parallel Manipulators With Hidden Revolute Joints

作者：Li, Ju; McCarthy, J. Michael^*

来源：Journal of Mechanisms and Robotics, 2017, 9(3): 031007.

DOI：10.1115/1.4035542

• spherical parallel manipulator
• forward kinematics
• singularity variety
• Jacobian matrix
• dual quaternions
• homogeneous polynomial

In this paper, we examine two spherical parallel manipulators (SPMs) constructed with legs that include planar and spherical subchains that combine to impose constraints equivalent to hidden revolute joints. The first has supporting serial chain legs constructed from three revolute joints with parallel axes, denoted R parallel to R parallel to R, followed by two revolute joints that have intersecting axes, denoted (R) over cap(R) over cap. The leg has five degrees-of-freedom and is denoted R parallel to R parallel to R-(R) over cap(R) over cap. Three of these legs can be assembled so the spherical chains all share the same point of intersection to obtain a spherical parallel manipulator denoted as 3-R parallel to R parallel to R-(R) over cap(R) over cap. The second spherical parallel manipulator has legs constructed from three revolute joints that share one point of intersection, denoted (RRR) over cap, and a second pair of revolute joints with axes that intersect in a different point. This five-degree-of-freedom leg is denoted (RRR) over cap-(R) over cap(R) over cap. The spherical parallel manipulator constructed from these legs is 3-(RRR) over cap-(R) over cap(R) over cap. We show that the internal constraints of these two types of legs combine to create hidden revolute joints that can be used to analyze the kinematics and singularities of these spherical parallel manipulators. A quaternion formulation provides equations for the quartic singularity varieties some of which decompose into pairs of quadric surfaces which we use to classify these spherical parallel manipulators.

• 出版日期2017-6
• 单位常州大学