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Research Papers

Design Criteria for Serial Chain Mechanisms Based on Kinetic Energy Ratios

[+] Author and Article Information
Oziel Rios1

Department of Mechanical Engineering, Robotics Research Group, University of Texas at Austin, Austin, TX 78758jrios90610@yahoo.com

Delbert Tesar

Department of Mechanical Engineering, Robotics Research Group, University of Texas at Austin, Austin, TX 78758tesar@mail.utexas.edu

In this work, we consider mechanisms whose joints are of the same type (all rotary or all prismatic) so that all the elements of $φ̇$ have homogeneous units. The physical meaning of the eigenvalues of a matrix with inhomogeneous units is not addressed in this work.

Note that rigid body denotes both the link and actuator.

In literature MOT is referred to as the measure of manipulability (MOM). In this work, however, since the main application is design, MOT is used to make it clear to the reader that the mechanical gain associated with the mechanism’s geometry “transmits” the actuator and link parameters to the output.

1

Corresponding author.

J. Mech. Des 131(8), 081002 (Jul 09, 2009) (8 pages) doi:10.1115/1.3149846 History: Received June 26, 2008; Revised May 09, 2009; Published July 09, 2009

Abstract

In this article, a description of the kinetic energy partition values (KEPVs) of serial chain mechanisms, as well as their rates of change, is presented. The KEPVs arise from the partitioning of the mechanism’s kinetic energy and correspond to the critical values of the kinetic energy ratios of the actuators and links and are indicators of the kinetic energy distribution within the system while the rates of change in the KEPVs indicate the sensitivity to change in the location of that kinetic energy. A high value for the KEPV rate of change together with a high operational state implies that the amount of kinetic energy flowing in the system is large, further implying a loss of precision in the system due to large inertial torques being generated. The KEPVs and their rates can be used to identify the actuators whose parameters (mass, inertia, and mechanical gain) greatly affect the overall distribution of kinetic energy within the system, thereby allowing the designer to optimize these actuators to improve the performance of the overall mechanism. Two design criteria, one based on the KEPVs and another based on their rates of change, are developed. A two degree-of-freedom (DOF) planar mechanism is used to demonstrate the concepts and to verify the properties of the KEPVs and their rates. Also, a 6DOF spatial manipulator is used to illustrate the solution of a multicriteria design optimization problem where two conflicting criteria are considered: a KEPV criterion and an effective mass criterion. The goal of the design problem is to demonstrate how the inertial parameters of the actuators and the mechanical gains of the actuator transmissions alter the kinetic energy of the system both in terms of its magnitude, which is “measured” via the effective mass criterion, and its distribution, which is measured via the KEPV criterion. It is demonstrated that the mechanical gains in the actuators significantly influence the magnitude of the kinetic energy as well as its distribution within the system due to the inertial amplification. The KEPVs and their rates of change provide a novel new approach to analyzing the dynamic character of serial chain mechanisms.

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Figures

Figure 1

Serial chain mechanism

Figure 2

2DOF serial mechanism

Figure 3

Plots of KEPV criterion det(Γ) with respect to (a) joint position φ2 and (b) reduction ratio G1

Figure 4

Plots of KEPV rate criterion tr(Ξ2) with respect to (a) joint position φ2 and (b) reduction ratio G1

Figure 5

6DOF Puma type manipulator

Figure 6

Pareto curve of normalized optimal solutions demonstrating trade-offs between solutions. Note that x-axis is normalized.

Errata

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