Geometric design of motions constrained by a contacting surface pair
✍ Scribed by Michael Hofer; Helmut Pottmann; Bahram Ravani
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 874 KB
- Volume
- 20
- Category
- Article
- ISSN
- 0167-8396
No coin nor oath required. For personal study only.
✦ Synopsis
We discuss the following problem which arises in robot motion planning, NC machining and computer animation: Given are a fixed surface Ψ and N positions Φ i of a moving surface Φ such that the Φ i are in point contact with Ψ . Compute a smooth and fair Euclidean gliding motion Φ(t) of the surface Φ on the surface Ψ which interpolates (or approximates) the given positions Φ i at time instances t i . First we generalize interpolatory variational subdivision algorithms for curves to curves on surfaces. Second we study an unconstraint motion design algorithm which we then extend to the main contribution of this paper, an algorithm for the design of a motion constraint by a contacting surface pair. Both motion design algorithms use a feature point representation of the moving surface, subdivision algorithms for curves, instantaneous kinematics, and ideas from line geometry. Geometric methods are used for the numerical solution of the arising optimization problems.