New Homotopy Solution Techniques Applied to Variable Geometry Trusses

Abstract

A VGT, or Variable Geometry Truss, can be thought of as a statically determinate truss that has been modified to contain some number of variable length members. These extensible members allow the truss to vary its configuration in a controlled manner. Some of the typical applications envisioned for VGTs are booms to position equipment in space, as supports for space antennae, and as berthing devices. Recently, they have also been proposed as parallel-actuated, long-chain, high dexterity manipulators. This paper will demonstrate the use of homotopy continuation in solving the kinematics of relatively complex variable geometry trusses (VGTs), including the octahedron and the decahedron. The procedural aspects are described in detail with the help of examples. Results of the example problems are also presented.