Abstract
In general, constraint equations are needed for the inverse kinematics (IK) of the parallel mechanism (PM) with less than 6 degrees of freedom (DOF) and dependent parameters describing the pose of the moving platform. However, the applicability of such an approach is restricted to the mechanism configuration from which the constraint equations are derived. In order to solve this problem, this paper presents an iterative method for solving the IK of a 3-limb parallel mechanism with 3 DOF. Therefore, a kinematically equivalent mechanism, which is a virtual model composed of a 6-limb parallel mechanism with 6 DOF under the active joint motion constraint, is introduced. In this method, an iterative procedure for the IK of a 3-PRS parallel mechanism using the IK of the kinematically equivalent mechanism is proposed. Numerical examples demonstrate the convergence process during iteration, the ability to obtain all solutions, and the applicability to various structural parameters of the proposed method.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Hunt, K.H.: Structural Kinematics of in- parallel-actuated robot-arms. J. Mech. Transm. Autom. Des. 105(4), 705–712 (1983)
Bonev I.A., Zlatanov D., Gosselin C.M.: Advantages of the modified euler angles in the design and control of PKMs. In: Parallel Kinematic Machines International Conference, pp. 171–188 (2002)
Lee, K.M., Shah, D.K.: Kinematic analysis of a three degrees of freedom in-parallel actuated manipulator. IEEE J. Robot. Autom. 4(3), 354–360 (1988)
Bürüncük, K., Tokad, Y.: On the kinematic of a 3-DOF stewart platform. J. Field Robot. 16(2), 105–118 (1999)
Sokolov, A., Xirouchakis, P.: Kinematics of a 3-DOF parallel manipulator with an R-P-S joint structure. Robotica 23(2), 207–217 (2005)
Nanua, P., Waldron, K.J., Murthy, V.: Direct kinematic solution of a stewart platform. IEEE Trans. Robot. Autom. 6(4), 438–444 (1990)
Takeda, Y., Liang, X.: Transmission index of lower-mobility parallel mechanism: case study on 3-PRS mechanism. In: ASME 2017 IDECT/CIE Conference. ASME, USA (2017)
Russo, M., Ceccarelli, M., Takeda, Y.: Force transmission and constraint analysis of a 3-SPR parallel manipulator. In: Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 954406217750190 (2017)
Takeda, Y., Funabashi, H.: Motion Transmissibility of In-Parallel Actuated Manipulators. JSME Int. J. Ser. C, Dyn. Control Robot., Des. Manuf., 38(4), 749–755 (1995)
Li, Y., Xu, Q.: Kinematic analysis of a 3-PRS parallel manipulator. Robot. Comput.-Integrated Manuf. 23(4), 395–408 (2007)
Li, Q., Chen, Z., Chen, Q., Wu, C., Hu, X.: Parasitic motion comparison of 3-PRS parallel mechanism with different limb arrangements. Robot. Comput.-Integr. Manuf. 27(2), 389–396 (2011)
Lukanin, V.: Inverse kinematics, forward kinematics and working space determination of 3DOF parallel manipulator with S-P-R joint structure. Period. Polytech. Eng. Mech. Eng. 49(1), 39–61 (2005)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Liang, X., Takeda, Y. (2019). Iterative Method for the Inverse Kinematics of a 3-Limb Parallel Mechanism with 3-DOF Using a 6-Limb Mechanism with 6-DOF. In: Lenarcic, J., Parenti-Castelli, V. (eds) Advances in Robot Kinematics 2018. ARK 2018. Springer Proceedings in Advanced Robotics, vol 8. Springer, Cham. https://doi.org/10.1007/978-3-319-93188-3_13
Download citation
DOI: https://doi.org/10.1007/978-3-319-93188-3_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-93187-6
Online ISBN: 978-3-319-93188-3
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)