A pair of equilateral tetrahedra is formed by drawing all the face diagonals of a cube. Holding one tetrahedron fixed, the motion of the other one is investigated, subject to the constraint that edges formed by the diagonals of the same cube face remain coplanar, i.e., intersect or coincide. / Based entirely on the solution of equations arising directly from this constraint, displacement of the movable tetrahedron is expressed as rigid body rotation with translation. This original result forms the foundation upon which kinematic and dynamic analyses are built: (1) Edge pair intersections are expressed in closed, parametric form so as to facilitate further investigation. (2) A closed-form solution for the two degree-of-freedom workspace boundary is obtained by evaluating conditions under which these parameters approach zero or one. This important extension of previous research is necessary to control the motion of any hardware implementation of a double tetrahedral mechanism. (3) Inverse kinematics, which concerns the motion of such a mechanism, is presented. Two kinds of singularity, basic position singularity and overlapping singularity, are discussed from the point of view of the Jacobian matrices. (4) Given a wrench applied to the movable frame, the system of reactive forces or torques needed at the joints, i.e., the edge intersections, is determined. (5) Using the Lagrangian formulation, the inverse dynamics of this mechanism are derived and simulation results are presented. (6) The possible application of the double tetrahedral mechanism as a two degree-of-freedom manipulator joint is discussed.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.60590 |
| Date | January 1991 |
| Creators | Chen, Huan-Wei |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Master of Engineering (Department of Mechanical Engineering.) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 001258340, proquestno: AAIMM72191, Theses scanned by UMI/ProQuest. |
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