Abstract
This paper presents a solution to the forward position problem of two PUMA-type robots manipulating a Bennett linkage payload. The orientation of a specified payload link is described by a sixth-order polynomial and a specified angular joint displacement in the wrist subassembly of one of the robots is described by a second-order polynomial. A solution technique, based on orthogonal transformation matrices with dual number elements, is used to obtain closed-form solutions for the remaining unknown angular joint displacements in the wrist subassembly of each robot. The paper shows that, for a given set of robot input angles, twenty-four assembly configurations of the robot-payload system are possible. The polynomials provide insight into these configurations, and also reveal stationary configurations of the system. The paper emphasizes that insight into the kinematic geometry of the system is essential in developing the forward position solution. Graphical methods are presented which provide insight into the geometry, and a check of the analytical approach. For illustrative purposes, a numerical example of the two robots manipulating a Bennett linkage is included in this paper to demonstrate the importance of the polynomials and the closed-form solutions.
