The kinematic problems associated with two cooperating robots manipulating closed-loop linkage payloads
Abstract
This dissertation is a study of the kinematic problems associated with two cooperating robots manipulating closed-loop linkage payloads. The solutions to the forward position problem and the forward and inverse velocity problems are first presented for two 3-revolute robots manipulating a planar four-bar linkage payload. The orientation of a specified link in the payload is described by a sixth-order polynomial. The polynomial contains information regarding the assembly and the stationary configurations of the system. Solutions to the forward and inverse velocity problems are formulated using two Jacobian matrices: one associated with the robot input joint rates, and the other associated with the payload output rates. To provide insight into the system, both Jacobian matrices are obtained from geometric inspection. A procedure to obtain the inverse of each Jacobian matrix from geometric inspection is also developed. This procedure uses first-order kinematic coefficients and the principle of superposition. The kinematic coefficients are expressed in terms of instantaneous centers of zero velocity to provide geometric insight into the system. An investigation of the singular and stationary configurations of the system is included, and the geometric interpretation of these configurations is emphasized. A closed-form solution to the forward position problem is then presented for two PUMA-type robots manipulating a planar four-bar linkage payload. The orientation of a specified payload link is described by a sixth-order polynomial and a specified angular displacement in a robot end-effector 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. Graphical techniques are used to illustrate that, for a given set of input angles, twenty-four assembly configurations of the robot-payload system are possible. Finally, a closed-form solution to the forward position problem for two PUMA-type robots manipulating a spatial Bennett linkage payload is presented. For illustrative purposes, numerical examples are presented to demonstrate the solution procedures developed for the forward position problem and the velocity problems investigated in the dissertation.
Degree
Ph.D.
Advisors
Pennock, Purdue University.
Subject Area
Mechanical engineering|Industrial engineering
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