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| Content Provider | The American Society of Mechanical Engineers (ASME) Digital Collection |
|---|---|
| Author | Purwar, Anurag Jin, Zhe Ge, Qiaode Jeffrey |
| Copyright Year | 2008 |
| Abstract | In the recent past, we have studied the problem of synthesizing rational interpolating motions under the kinematic constraints of any given planar and spherical 6R closed chain. This work presents some preliminary results on our initial attempt to solve the inverse problem, that is to determine the link lengths of planar and spherical 6R closed chains that follow a given smooth piecewise rational motion under the kinematic constraints. The kinematic constraints under consideration are workspace related constraints that limit the position of the links of planar and spherical closed chains in the Cartesian space. By using kinematic mapping and a quaternions based approach to represent displacements of the coupler of the closed chains, the given smooth piecewise rational motion is mapped to a smooth piecewise rational curve in the space of quaternions. In this space, the aforementioned workspace constraints on the coupler of the closed chains define a constraint manifold representing all the positions available to the coupler. Thus the problem of dimensional synthesis may be solved by modifying the size, shape and location of the constraint manifolds such that the mapped rational curve is contained entirely inside the constraint manifolds. In this paper, two simple examples with preselected moving pivots on the coupler as well as fixed pivots are presented to illustrate the feasibility of this approach. |
| Sponsorship | Design Engineering Division and Computers in Engineering Division |
| Starting Page | 707 |
| Ending Page | 715 |
| Page Count | 9 |
| File Format | |
| ISBN | 9780791843260 |
| DOI | 10.1115/DETC2008-49947 |
| e-ISBN | 0791838315 |
| Volume Number | Volume 2: 32nd Mechanisms and Robotics Conference, Parts A and B |
| Conference Proceedings | ASME 2008 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference |
| Language | English |
| Publisher Date | 2008-08-03 |
| Publisher Place | Brooklyn, New York, USA |
| Access Restriction | Subscribed |
| Subject Keyword | Manifolds Chain Interpolation Inverse problems Shapes Kinematics |
| Content Type | Text |
| Resource Type | Article |
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