Using the Singularity Trace to Understand Linkage Motion Characteristics

Using the Singularity Trace to Understand Linkage Motion Characteristics

Bibliographic Details
Main Author: Li, Lin
Language:English
Published: University of Dayton / OhioLINK 2013
Subjects:
Mechanical Engineering
Mathematics
Watt II
Stephenson III
double butterfly
singularity
mathematical modeling
motion curve
singularity trace
Online Access:http://rave.ohiolink.edu/etdc/view?acc_num=dayton1366634758
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spelling ndltd-OhioLink-oai-etd.ohiolink.edu-dayton13666347582021-08-03T05:22:27Z Using the Singularity Trace to Understand Linkage Motion Characteristics Li, Lin Mechanical Engineering Mathematics Watt II Stephenson III double butterfly singularity mathematical modeling motion curve singularity trace This thesis provides examples of a new method used to analyze the motion characteristics of single-degree-of-freedom, closed-loop linkages with a designated input angle and one or two design parameters. The method involves the construction of a singularity trace, which is a plot that reveals changes in the number of geometric inversions, singularities, and changes in the number of branches as a design parameter is varied. This thesis applies the method to planar linkages such as the Watt II, Stephenson III and double butterfly, and spatial linkages such as spherical four-bar and Revolute-Cylindrical-Cylindrical-Cylindrical (RCCC) linkages. Results from this investigation include the following. Special instances of the singularity trace for the Watt II linkage include multiple coincident projections of the singularity curve and symmetric characteristics of the singularity trace for special design parameters. For the Stephenson III and double butterfly linkages, instances where the input angle is able to rotate more than one revolution between singularities have been identified. This characteristic demonstrates a net-zero, singularity free activation sequence that places the mechanism into a different geometric inversion. Additional observations from the examples show that net-zero, singularity free activation sequences can occur in the motion curves with " U " or " S " shapes. Cases are shown where subtle changes to two design parameters of a Stephenson III linkage drastically alter the motion. Additionally, isolated critical points are found to exist for the double butterfly, where the linkage becomes a structure and looses the freedom to move. This thesis also applies this method to spatial linkages to analyze a spherical mechanism. The structure of the loop closure equations was modified to accommodate a third, spatial coordinate. An example is provided that uses a spherical four-bar linkage. The singularity map has been found to be similar to a comparable planar four-bar case. Lastly, loop closure and singularity equations have been formulated to address a truly spatial linkage, the RCCC. A solution method has been identified. The analysis is listed in future work. 2013-05-23 English text University of Dayton / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=dayton1366634758 http://rave.ohiolink.edu/etdc/view?acc_num=dayton1366634758 unrestricted This thesis or dissertation is protected by copyright: some rights reserved. It is licensed for use under a Creative Commons license. Specific terms and permissions are available from this document's record in the OhioLINK ETD Center.
collection NDLTD
language English
sources NDLTD
topic Mechanical Engineering
Mathematics
Watt II
Stephenson III
double butterfly
singularity
mathematical modeling
motion curve
singularity trace
spellingShingle Mechanical Engineering
Mathematics
Watt II
Stephenson III
double butterfly
singularity
mathematical modeling
motion curve
singularity trace
Li, Lin
Using the Singularity Trace to Understand Linkage Motion Characteristics
author Li, Lin
author_facet Li, Lin
author_sort Li, Lin
title Using the Singularity Trace to Understand Linkage Motion Characteristics
title_short Using the Singularity Trace to Understand Linkage Motion Characteristics
title_full Using the Singularity Trace to Understand Linkage Motion Characteristics
title_fullStr Using the Singularity Trace to Understand Linkage Motion Characteristics
title_full_unstemmed Using the Singularity Trace to Understand Linkage Motion Characteristics
title_sort using the singularity trace to understand linkage motion characteristics
publisher University of Dayton / OhioLINK
publishDate 2013
url http://rave.ohiolink.edu/etdc/view?acc_num=dayton1366634758
work_keys_str_mv AT lilin usingthesingularitytracetounderstandlinkagemotioncharacteristics
_version_ 1719419017654960128

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