Abstract
Higher-order derivatives of kinematic mappings give insight into the motion characteristics of complex mechanisms. Screw theory and its associated Lie group theory have been used to find these derivatives of loop closure equations up to an arbitrary order. In this paper, this is extended to the higher-order derivatives of the solution to these loop closure equations to provide an approximation of the finite motion of serial and parallel mechanisms. This recursive algorithm, consisting solely of matrix operations, relies on a simplified representation of the higher-order derivatives of open chains. The method is applied to a serial, a multi-DOF parallel, and an overconstrained mechanism. In all cases, adequate approximation is obtained over a large portion of the workspace.
Original language | English |
---|---|
Pages (from-to) | 1190-1201 |
Number of pages | 12 |
Journal | Robotica |
Volume | 37 |
Issue number | 7 |
Early online date | 29 Jun 2018 |
DOIs | |
Publication status | Published - 1 Jul 2019 |
Keywords
- UT-Hybrid-D
- Bennet linkage
- Higher-order kinematics
- Screw theory
- Taylor approximation
- 5-bar mechanism