A Polynomial Formulation of Inverse Kinematics of Rolling Contact
Rolling contact has been used by robotic devices to drive between configurations. The degrees of freedom (DOFs) of rolling contact pairs can be one, two, or three, depending on the geometry of the objects. This paper aimed to derive three kinematic inputs required for the moving object to follow a t...
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| Format: | Journal Article |
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ASME International
2015
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| Online Access: | http://hdl.handle.net/20.500.11937/38735 |
| _version_ | 1848755400342503424 |
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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 | Rolling contact has been used by robotic devices to drive between configurations. The degrees of freedom (DOFs) of rolling contact pairs can be one, two, or three, depending on the geometry of the objects. This paper aimed to derive three kinematic inputs required for the moving object to follow a trajectory described by its velocity profile when the moving object has three rotational DOFs and thus can rotate about any axis through the contact point with respect to the fixed object. We obtained three contact equations in the form of a system of three nonlinear algebraic equations by applying the curvature theory in differential geometry and simplified the three nonlinear algebraic equations to a univariate polynomial of degree six. Differing from the existing solution that requires solving a system of nonlinear ordinary differential equations, this polynomial is suitable for fast and accurate numerical root approximations. The contact equations further revealed the two essential parts of the spin velocity: The induced spin velocity governed by the geometry and the compensatory spin velocity provided externally to realize the desired spin velocity. |
| first_indexed | 2025-11-14T08:55:42Z |
| format | Journal Article |
| id | curtin-20.500.11937-38735 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T08:55:42Z |
| publishDate | 2015 |
| publisher | ASME International |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-387352017-09-13T14:15:45Z A Polynomial Formulation of Inverse Kinematics of Rolling Contact Cui, Lei Dai, J. kinematics mobile robot rolling differential geometry Darboux frame contact polynomial Rolling contact has been used by robotic devices to drive between configurations. The degrees of freedom (DOFs) of rolling contact pairs can be one, two, or three, depending on the geometry of the objects. This paper aimed to derive three kinematic inputs required for the moving object to follow a trajectory described by its velocity profile when the moving object has three rotational DOFs and thus can rotate about any axis through the contact point with respect to the fixed object. We obtained three contact equations in the form of a system of three nonlinear algebraic equations by applying the curvature theory in differential geometry and simplified the three nonlinear algebraic equations to a univariate polynomial of degree six. Differing from the existing solution that requires solving a system of nonlinear ordinary differential equations, this polynomial is suitable for fast and accurate numerical root approximations. The contact equations further revealed the two essential parts of the spin velocity: The induced spin velocity governed by the geometry and the compensatory spin velocity provided externally to realize the desired spin velocity. 2015 Journal Article http://hdl.handle.net/20.500.11937/38735 10.1115/1.4029498 ASME International restricted |
| spellingShingle | kinematics mobile robot rolling differential geometry Darboux frame contact polynomial Cui, Lei Dai, J. A Polynomial Formulation of Inverse Kinematics of Rolling Contact |
| title | A Polynomial Formulation of Inverse Kinematics of Rolling Contact |
| title_full | A Polynomial Formulation of Inverse Kinematics of Rolling Contact |
| title_fullStr | A Polynomial Formulation of Inverse Kinematics of Rolling Contact |
| title_full_unstemmed | A Polynomial Formulation of Inverse Kinematics of Rolling Contact |
| title_short | A Polynomial Formulation of Inverse Kinematics of Rolling Contact |
| title_sort | polynomial formulation of inverse kinematics of rolling contact |
| topic | kinematics mobile robot rolling differential geometry Darboux frame contact polynomial |
| url | http://hdl.handle.net/20.500.11937/38735 |