Modelling flexible link manipulators in the three-dimensional space
Abstract
The force/torque relationship between the joints and the end effector of flexible link manipulators is affected not only by the motion of the joints but also by translations and rotations of the links due to their bending and torsion effects. These inaccuracies in the force/torque relationship for flexible manipulators in the three-dimensional space are addressed. This thesis presents the development of a systematic technique for determining the force/torque relationship between the joints and the end effector for flexible link manipulators. The proposed technique accounts for link bending and torsion in the kinematic equations of a flexible manipulator while considering rigid hubs and tools attached to the ends of the links. A procedure for modelling link bending and torsion to within a desired accuracy has also been developed. The resulting model is independent of manipulator configuration. In this technique, vector cross products are used instead of partial derivatives. This reduces inaccuracies which result from approximations made in the kinematic equations when modelling bending and torsion of the links. The magnitude and location of these inaccuracies are characterized. The validity of the proposed technique/procedure and the inaccuracies noted are demonstrated for link bending of a single-link planar manipulator by comparing simulations of the resulting force/torque relationships to results obtained experimentally; however, the experiments were not able to illustrate the torsion effect in the proposed model. Results indicate that the magnitude and location of the errors in the force/torque relationship are dependent upon the rotation due to link deformation, the "length" of the rest of the manipulator, and the configuration of the manipulator. Although the proposed technique is able to account for the link bending and torsion effects in the kinematic equations of a flexible manipulator, it also suffers from several limitations. These include: translations and rotations due to link deformation are required to be "small"; no analytical equation is given for determining the amount of error required to divide a link into elements nor is the exact location of the division given for the bending and torsion models; and the "body forces" due to the weight of the links are not considered in the force/torque relationship.
Degree
Ph.D.
Advisors
Mahil, Purdue University.
Subject Area
Electrical engineering|Mechanical engineering|Mechanics
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