Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Computer-Aided Design of Rational Motions for 4R and 6R Spatial Mechanism Synthesis

Daniel Huczala, Severinas Zube, Martin Pfurner, Johannes Siegele, Frank C. Park

TL;DR

A new interpolation scheme for seven 3D points based on cubic quaternionic Bezier curves is introduced, which admits factorization, i.e. the synthesis of a spatial six-bar mechanism whose tool frame passes the specified seven points.

Abstract

This paper focuses on geometric methods for generating rational motions used in the design of single-loop rational linkages, 1-degree-of-freedom mechanisms that can execute prescribed spatial tasks. Building on established rational motion synthesis methods, we introduce a new interpolation scheme for seven 3D points based on cubic quaternionic Bezier curves. The resulting motion admits factorization, i.e. the synthesis of a spatial six-bar mechanism whose tool frame passes the specified seven points. To support engineering practice, we provide open-source CAD tools that implement also the other methods and provide fast visual evaluation of motion generation and mechanism synthesis.

Computer-Aided Design of Rational Motions for 4R and 6R Spatial Mechanism Synthesis

TL;DR

A new interpolation scheme for seven 3D points based on cubic quaternionic Bezier curves is introduced, which admits factorization, i.e. the synthesis of a spatial six-bar mechanism whose tool frame passes the specified seven points.

Abstract

This paper focuses on geometric methods for generating rational motions used in the design of single-loop rational linkages, 1-degree-of-freedom mechanisms that can execute prescribed spatial tasks. Building on established rational motion synthesis methods, we introduce a new interpolation scheme for seven 3D points based on cubic quaternionic Bezier curves. The resulting motion admits factorization, i.e. the synthesis of a spatial six-bar mechanism whose tool frame passes the specified seven points. To support engineering practice, we provide open-source CAD tools that implement also the other methods and provide fast visual evaluation of motion generation and mechanism synthesis.
Paper Structure (10 sections, 23 equations, 1 figure)

This paper contains 10 sections, 23 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Mathematical Preliminaries
  3. Methods to Construct Rational Motions
  4. Quadratic Motion through 3 Poses
  5. Cubic Motion through 4 Poses
  6. Motion through 2n+1 Points
  7. Quadratic Motion through 5 Points
  8. Cubic Motion through 7 Points
  9. Implementation
  10. Conclusion

Figures (1)

  • Figure 1: Left: Motion Designer -- an interactive plot of a 1-DoF motion that interpolates 7 given points (purple); right: example of a produced 6R prototype.