New Kinematic Construction Links Serial and Parallel Mechanisms
A novel framework integrates various kinematic principles for enhanced robotic motion analysis.
This research presents an innovative kinematic construction that unifies serial propagation, parallel-mechanism closure, and rigid-platform point fields within a dual screw framework. It retains a cylindrical joint as a fundamental physical block, with revolute and prismatic joints as specific instances.
Key Findings
The study employs ordinary Bell polynomials to organize derivatives of the exponential factor for fixed joint axes, maintaining the physical order of noncommuting factors across a chain. The paper also introduces covariant formulas for serial twist jets and a triangular active-passive closure recurrence for parallel mechanisms.
Validation and Results
Validation is achieved through various mechanisms, including a generic 3C chain and an RR+RRR spherical wrist, demonstrating high accuracy with residuals below $10^{-12}$ in SI units. The findings emphasize the kinematic nature of the formulation, applicable in regular configurations.