Direct Kinematics, Inverse Kinematics, and Motion Planning of 1-DoF Rational Linkages
<|reference_start|>Direct Kinematics, Inverse Kinematics, and Motion Planning of 1-DoF Rational Linkages: This study presents a set of algorithms that deal with trajectory planning of rational single-loop mechanisms with one degree-of-freedom (DoF). Benefiting from a dual quaternion representation of a rational motion, a formula for direct (forward) kinematics, a numerical inverse kinematics algorithm, and the generation of a driving-joint trajectory are provided. A novel approach using the Gauss-Newton search for the one-parameter inverse kinematics problem is presented. Additionally, a method for performing smooth equidistant travel of the tool is provided by applying arc-length reparameterization. This general approach can be applied to one-DoF mechanisms with four to seven joints characterized by a rational motion, without any additional geometrical analysis. An experiment was performed to demonstrate the usage in a laboratory setup.<|reference_end|>
@article{huczala2024direct,
    title={Direct Kinematics, Inverse Kinematics, and Motion Planning of 1-DoF
  Rational Linkages},
    author={Daniel Huczala, Andreas Mair, Tomas Postulka},
    journal={arXiv preprint arXiv:2409.01198},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.01198},
    primaryClass={cs.RO}
}