Axis Constraint Analysis and Its Resultant 6R Double-Centered Overconstrained Mechanisms
This paper investigates the 6R overconstrained mechanisms by looking at an arrangement that axes intersect at two centers with arbitrary intersection-angles. From the close-loop matrix equation of the mechanism, the paper develops a set of geometric constraint equations of the 6R double-centered ove...
| Main Authors: | , |
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| Format: | Journal Article |
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ASME Press
2011
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| Online Access: | http://hdl.handle.net/20.500.11937/41144 |
| _version_ | 1848756062850646016 |
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| author | Cui, Lei Dai, J. |
| author_facet | Cui, Lei Dai, J. |
| author_sort | Cui, Lei |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | This paper investigates the 6R overconstrained mechanisms by looking at an arrangement that axes intersect at two centers with arbitrary intersection-angles. From the close-loop matrix equation of the mechanism, the paper develops a set of geometric constraint equations of the 6R double-centered overconstrained mechanisms. This leads to the axis constraint equation after applying the Sylvester’s dialytic elimination method. The equation reveals the geometric constraint of link and axis parameters and identifies three categories of the 6R double-centered overconstrained mechanisms with arbitrary axis intersection-angles. The first two categories present two 6R double-centered overconstrained mechanisms and a 6R spherical mechanism. The last category evolves into the 6R double-spherical overconstrained mechanism with arbitrary axis intersection-angles at each spherical center. This further evolves into Baker’s double-Hooke mechanism and his derivative double-spherical mechanism with orthogonal axis intersection. The paper further develops the joint-space solution of the 6R double-centered overconstrained mechanisms based on the geometric constraint equation and verifies the result with a numerical example. |
| first_indexed | 2025-11-14T09:06:14Z |
| format | Journal Article |
| id | curtin-20.500.11937-41144 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:06:14Z |
| publishDate | 2011 |
| publisher | ASME Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-411442017-09-13T14:11:35Z Axis Constraint Analysis and Its Resultant 6R Double-Centered Overconstrained Mechanisms Cui, Lei Dai, J. closed-loop solution 6R mechanisms overconstrained Sylvester - elimination joint-space polynomial This paper investigates the 6R overconstrained mechanisms by looking at an arrangement that axes intersect at two centers with arbitrary intersection-angles. From the close-loop matrix equation of the mechanism, the paper develops a set of geometric constraint equations of the 6R double-centered overconstrained mechanisms. This leads to the axis constraint equation after applying the Sylvester’s dialytic elimination method. The equation reveals the geometric constraint of link and axis parameters and identifies three categories of the 6R double-centered overconstrained mechanisms with arbitrary axis intersection-angles. The first two categories present two 6R double-centered overconstrained mechanisms and a 6R spherical mechanism. The last category evolves into the 6R double-spherical overconstrained mechanism with arbitrary axis intersection-angles at each spherical center. This further evolves into Baker’s double-Hooke mechanism and his derivative double-spherical mechanism with orthogonal axis intersection. The paper further develops the joint-space solution of the 6R double-centered overconstrained mechanisms based on the geometric constraint equation and verifies the result with a numerical example. 2011 Journal Article http://hdl.handle.net/20.500.11937/41144 10.1115/1.4004225 ASME Press restricted |
| spellingShingle | closed-loop solution 6R mechanisms overconstrained Sylvester - elimination joint-space polynomial Cui, Lei Dai, J. Axis Constraint Analysis and Its Resultant 6R Double-Centered Overconstrained Mechanisms |
| title | Axis Constraint Analysis and Its Resultant 6R Double-Centered Overconstrained Mechanisms |
| title_full | Axis Constraint Analysis and Its Resultant 6R Double-Centered Overconstrained Mechanisms |
| title_fullStr | Axis Constraint Analysis and Its Resultant 6R Double-Centered Overconstrained Mechanisms |
| title_full_unstemmed | Axis Constraint Analysis and Its Resultant 6R Double-Centered Overconstrained Mechanisms |
| title_short | Axis Constraint Analysis and Its Resultant 6R Double-Centered Overconstrained Mechanisms |
| title_sort | axis constraint analysis and its resultant 6r double-centered overconstrained mechanisms |
| topic | closed-loop solution 6R mechanisms overconstrained Sylvester - elimination joint-space polynomial |
| url | http://hdl.handle.net/20.500.11937/41144 |