Direct Kinematics, Inverse Kinematics, and Motion Planning of 1-DoF Rational Linkages
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913869104939008 |
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| author | Huczala, Daniel Mair, Andreas Postulka, Tomas |
| author_facet | Huczala, Daniel Mair, Andreas Postulka, Tomas |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_01198 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Direct Kinematics, Inverse Kinematics, and Motion Planning of 1-DoF Rational Linkages Huczala, Daniel Mair, Andreas Postulka, Tomas Robotics 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. |
| title | Direct Kinematics, Inverse Kinematics, and Motion Planning of 1-DoF Rational Linkages |
| topic | Robotics |
| url | https://arxiv.org/abs/2409.01198 |