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| Content Provider | The American Society of Mechanical Engineers (ASME) Digital Collection |
|---|---|
| Author | Lee, Chung-Ching Lee, Jeng-Hsiung Lee, Po-Chih |
| Copyright Year | 2012 |
| Abstract | Focusing on the structural type of 6 ternary links and 9 revolute pairs (denoted 6T-9R), which stems from the commercialized Expanda-Triangles construction toy, we conduct in-depth study on the mobility constraints of the generalized planar 6T-9R paradoxical chains. According to Grübler criterion, the degree of freedom (DoF) of the chains of this type is minus 3 and they should have no constrained motion. However, due to the special dimensional constraints (Euclidean metric), some of such paradoxical mechanisms can still have the full-cycle mobility. To identify the dimensional constraints of mobility algebraically, we adopt a simple direct algebraic elimination approach to attain an eliminant of sixth-order polynomial in one variable only. The identity of polynomial whose coefficients are merely function of link lengths and structural angles produces six necessary dimensional constraints for movable 6T-9R paradoxical chain. One new and two existing paradoxical chains are revealed and their numerical examples are illustrated to show the correctness and validity of the proposed dimensional constraints. A novel generalized form of planar 6-bar paradoxical chain is disclosed too. |
| Sponsorship | Design Engineering Division Computers and Information in Engineering Division |
| Starting Page | 1579 |
| Ending Page | 1586 |
| Page Count | 8 |
| File Format | |
| ISBN | 9780791845035 |
| DOI | 10.1115/DETC2012-70916 |
| Volume Number | Volume 4: 36th Mechanisms and Robotics Conference, Parts A and B |
| Conference Proceedings | ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference |
| Language | English |
| Publisher Date | 2012-08-12 |
| Publisher Place | Chicago, Illinois, USA |
| Access Restriction | Subscribed |
| Subject Keyword | Chain Mechanical admittance Cycles Construction Degrees of freedom Algebra Polynomials |
| Content Type | Text |
| Resource Type | Article |
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