We introduce to computer graphics the Pseudo-Rigid-Body Mechanism (PRBM) and the chain algorithm from mechanical engineering, with a unified tutorial from disparate source materials. The PRBM has been used successfully to simplify the simulation of non-linearly elastic beams, using deflections of an analogous spring and rigid-body linkage. It offers computational efficiency as well as an automatic parameterization in terms of physically measurable, intuitive inputs which fit naturally into existing animation work flows for character articulation. The chain algorithm is a technique for simulating the deflection of complicated elastic bodies in terms of straight elastic elements, which has recently been extended to incorporate PRBM beam-elements in three dimensions. We present a new, mathematically equivalent optimization of the 3D PRBM chain algorithm, from its former asymptotic complexity of O(n^2) in the number of elements n, to O(n). We also extend an existing PRBM for combined moment-force loads to 3D, where the existing 3D PRBM chain algorithm was limited to 3D PRBM elements for a moment-only load. This optimization and extension are validated by duplicating prior experimental results, but substituting the new optimization and combined-load elements. Finally, a loose road-map is provided with several key considerations for future extension of the techniques to dynamic simulations.
College and Department
Physical and Mathematical Sciences; Computer Science
BYU ScholarsArchive Citation
Hall, Anthony R., "The Pseudo-Rigid-Body Model for Fast, Accurate, Non-Linear Elasticity" (2013). All Theses and Dissertations. 3869.
simulation, rigid-body, mass-spring, non-linear elasticity