Title

Synthesis techniques for coupler-driven planar and spherical single degree of freedom mechanisms

Date of Award

2011

Degree Name

Ph.D. in Mechanical Engineering

Department

Department of Mechanical and Aerospace Engineering

Advisor/Chair

Advisor: Andrew P. Murray

Abstract

This dissertation presents the foundation for the synthesis of coupler-driven single degree of freedom (DOF) planar and spherical mechanisms. A coupler-driver is a kinematic chain connected between the fixed link and any floating link of the mechanism which can be actuated to move the mechanism through the desired motion. For the scope of this work, the coupler-driver is a revolute-prismatic-revolute (RPR) chain for planar mechanisms and a spherical-prismatic-spherical (SPS) chain for spherical and spatial mechanisms. Coupler-drivers are a little investigated class of actuation that offer several benefits as alternates to traditionally operated mechanisms, which are driven by one of their constituent joints. Although many of the results discussed apply to general 1 DOF planar and spherical mechanisms, the planar four-bar (4R) and spherical four-bar (s4R) are presented in detail due to their use as fundamental machine elements. Coupler-drivers are shown to have several advantages in both the synthesis and operation of a mechanism. This work seeks to identify these benefits and demonstrate that coupler-driven mechanisms are a viable alternative. The coupler-driver may be synthesized to reduce either the internal loading of the mechanism or the actuation loads. The former reduces friction in the joints and the buckling and twisting moments of the links and the latter allows for a motor with reduced output loads. Secondly, actuation via an input torque at one of the joints of the mechanism requires that the associated link continually rotate in one direction over the motion. If this condition is not met, the mechanism suffers from a branching defect. As the branch defects of the mechanism do not affect the coupler-driver, the set of potential solution mechanisms may increase to include those that were previously excluded due to this defect. Furthermore, as the use of the coupler-driver decouples the kinematic synthesis from the actuator design, the designer can synthesize a mechanism with a more desirable kinematic profile and then design an optimized actuator for that mechanism. Comparisons of coupler-driven four-bar mechanisms to traditional four-bars driven by a torque at one of the joints are conducted for both the spherical and planar cases. Finally, a completely general formulation for the kinematic synthesis of the coupler-driver is presented as are general concepts for the static analysis and comparison between coupler- and noncoupler-driven mechanisms. These formulations work for any single parameter planar or spherical motion, including those motions generated by four-bar mechanisms. The set of fixed and moving pivots of the coupler-driver that may be paired to drive a moving frame along any given motion are derived, as well as a set of conditions under which the motion has no potential driving chains.

Keywords

Machinery, Kinematics of, Mechanical movements, Joints (Engineering)

Rights Statement

Copyright 2011, author

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