Abstract
This paper presents a simple and effective closed-form method for solving direct kinematics of parallel mechanism (PM) based on ordered single-open-chain units (SOCs). The method includes two steps. The first step is to establish the kinematic constraint equations that contain the least virtual variables of a PM, by using the modelling principle based on ordered SOCs. The second step is to derive and solve a nonlinear equation with one unknown from the constraint position equations by means of the software Mathematica. The method is applicable for direct kinematics of various complex planar and spatial PMs.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Jalón, J.G.D., Serna, M.A., Avilés, R.: Computer method for kinematic analysis of lower-pair mechanisms. Mech. Mach. Theory 16(5), 543–566 (1981)
Kinzel, G.L., Chang, C.: The analysis of planar linkage using a modular approach. Mech. Mach. Theory 19(1), 165–172 (1984)
Yang, T.L.: A method of kinematic analysis by arbitrarilly prescribed input and application to planer multi-loop chains. In: Proceedings of the 6th World Congress on T.M.M., vol. 1, pp. 195–198 (1983)
Shen, H.P., Ding, K.L., Yang, T.L.: Configuration analysis of complex planar linkages and manipulators. Mech. Mach. Theory 35(3), 353–362 (2000)
Liu, A.X., Yang, T.L.: Kinematic Design of Mechanical System. China Petrochemical Press, Beijing (1999)
Husty, M., Pfurner, M., Schrocker, H.-P., Brunnthaler, K.: Algebraic methods in mechanism analysis and synthesis. Robotica 25(6), 639–640 (2007)
Rojas, N., Thomas, F.: On closed-form Solutions to the position analysis of baranov trusses. Mech. Mach. Theory 50, 179–196 (2012)
Shen, H.P., Yin, H.B., Wang, Z.: Research on forward position solutions for 6-SPS parallel mechanisms based on topology structure analysis. J. Mech. Eng. 49(21), 71–80 (2013)
Yang, T., Liu, A.X., Shen, H.P., Hang, L.B., Luo, Y.F., Jin, Q.: Topology Design of Robot Mechanisms. Springer, Singapore (2018)
Shen, H.P.: The kinematics of parallel mechanism by the modeling method based on the ordered SOCS. Center for modern institutional studies, Changzhou University, research report (2016)
Gosselin, C.M., Wang, J.: Static balancing of spatial six-degree-of-freedom parallel mechanisms with revolute actuators. J. Robot. Syst. 17(3), 159–170 (2000)
Acknowledgments
This research was possible thanks to support from the NSFC (No. 51475050 and 51375062). The first author thanks Prof. Federico Thomas and Prof. Andres. Kecskemethy for their useful discussions.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Shen, H., Xu, K., Wu, G., Yang, Tl. (2019). A Simple and General Closed-Form Method for Direct Kinematics of Mechanism Based on SOC Modeling. In: Gasparetto, A., Ceccarelli, M. (eds) Mechanism Design for Robotics. MEDER 2018. Mechanisms and Machine Science, vol 66. Springer, Cham. https://doi.org/10.1007/978-3-030-00365-4_2
Download citation
DOI: https://doi.org/10.1007/978-3-030-00365-4_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-00364-7
Online ISBN: 978-3-030-00365-4
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)