Structural Synthesis and Low-Cost Sensor Structure for Hexapods
Final Report Abstract
The focus in the project was on solving the forward kinematics of parallel mechanisms. It became apparent that this topic still had significant gaps in the relevant literature, which were uncovered during the course of the project and filled by our own publications in renowned journals and at world-renowned conferences. Initially, the focus here was on the forward kinematics of hexapods. However, it was shown that the presented solution approach can be generalized to general parallel kinematics. This was demonstrated using the example of planar 3-RPR parallel kinematics. By not measuring the lengths of the linear actuators and using suitable coordinates, the forward kinematics can be solved quickly and unambiguously. Even with very low-cost and low-resolution IMUs, the position of the working platform of a parallel kinematic can be determined quickly and relatively accurately. The method for solving the forward kinematics of parallel kinematics and, in particular, hexapods, i.e., determining the position (location and orientation) of the working platform exclusively by using the orientations of the working platform and the orientations of the linear drives, has been filed with the German Patent Office. With the help of the formulation developed in the project, the forward kinematics of parallel mechanisms can be solved much more simply and, above all, unambiguously. The only obstacle to its use in industry is the relatively large measurement errors associated with the use of inexpensive inertial sensors. The second major topic of the project was the computation of passive rotation when using universal joints in parallel mechanisms. This topic has been poorly addressed in the literature, but has a tremendous impact on the achievable accuracy of parallel kinematics. Numerous possible formulations of the problem were presented and compared with respect to their performance. In the third part of the project, the kinematic model was to be formulated using quaternions in order to reduce computation time and rounding errors during motion. In the course of the investigations it was found that the determination of the "passive rotation" is already applied. Here, classical methods based on sine and cosine are introduced, which are mathematically less accurate and, above all, more problematic than the use of quaternions due to the discontinuity ("gimble lock effect"). A general formulation of the kinematics is therefore useful and can be easily implemented by existing software (Matlab, Python etc.).
Publications
- Comparison of three methods of length compensation in a parallel kinematic and their equivalence conditions. MATEC Web of Conferences, 198:02003, 2018
Du, S.; Schlattmann, J.; Schulz, S.; Seibel, A.
(See online at https://doi.org/10.1051/matecconf/201819802003) - On the direct kinematics problem of parallel mechanisms. Journal of Robotics, 9 pages, 2018
Seibel, A., Schulz, S., Schlattmann, J.
(See online at https://doi.org/10.1155/2018/2412608) - On the origin of passive rotation in rotational joints, and how to calculate it. In Proceedings in Applied Mathematics and Mechanics, 19(1):e201900298, 2019
Du, S.; Schlattmann, J.; Schulz, S.; Seibel, A.
(See online at https://doi.org/10.1002/pamm.201900298) - Passive rotation of rotational joints and its computation method. In: Uhl, T. (Hrsg.): Advances in Mechanism and Machine Science. IFToMM WC 2019. Mechanisms and Machine Science, Band 73, Springer, Cham, S. 357–366, 2019
Du, S.; Schlattmann, J.; Schulz, S.; Seibel, A.
(See online at https://doi.org/10.1007/978-3-030-20131-9_36) - Solution for the direct kinematics problem of the general Stewart-Gough platform by using only linear actuators’ orientations. In: Lenarcic, J.; Parenti-Castelli, V. (Hrsg.): Advances in Robot Kinematics 2018. ARK 2018. Springer Proceedings in Advanced Robotics, Band 8, Springer, Cham, S. 56– 64, 2019
Schulz, S.; Seibel, A.; Schlattmann, J.
(See online at https://doi.org/10.1007/978-3-319-93188-3_7)
