Inverse Position Procedure for Manipulators with Rotary Joints

Abstract

Industrial robot manipulators are essentially spatial linkages that consist of rigid bodies connected by joints. Even though many types of joints (which are also known as kinematic pairs) are available for use in mechanical linkages, only two types are employed for robot manipulators. These are the revolute, or rotary, joints (referred to in literature as R) and the prismatic, or sliding, joints (referred to as P). These specific types allow a single degree of freedom relative movement between adjacent bodies; and are easier to drive and control than other kinematic pairs. Normally every joint on the manipulator is independently driven by a dedicated motor. It is central to kinematic control of manipulators to calculate the sets of joint-motor displacements which correspond to a desired pose (i.e. position and orientation) at the end-effector. The mathematical procedure which is followed to achieve this purpose is often referred to as, Inverse Position Analysis. This analysis presents a special difficulty in the field of Robotics as it is associat ed with the use of intricate spatial geometry techniques. The complexity of the analysis increases substantially with the number of rotary joints on the manipulator structure. For this reason a considerable part of the published literature is mainly concerned with the revolute-joint manipulators. Published literature reveals that various methods have been proposed to solve the inverse position problem of mani pulators. These methods range from Jacobian-based iterative techniques to highly sophisticated levels of equationmanipulation intended to reduce the whole model into a polynomial with thousands of mathematical terms. However, most industrial robots are designed with geometric features (such as parallelism and perpendicularity) to make it possible for simple inverse position solutions to be obtained in closed forms suitable for real time control. Another geometric aspect that leads to simplified inverse solutions is the spherical wrist design, which entails that the last three joints on the manipulator structure intersect at one point. This usually suggests that these three joints (also known as the wrist joints) have the main task of orienting (rather than placing) the end-effector in space. In this