The Mobility Analysis of a 3-CCR Parallel Manipulator with Three Screw-Type Terminal Constraints
Source abstract
Abstract
In the traditional three DOFs (degrees of freedom) PMs (parallel manipulators), the terminal constraints are constraint forces and torques. A recent study showed that the terminal constraints of some three DOFs PMs are screw-type constraints. However, determining the mobility of this class of PMs remains challenging. In order to solve the above problems, this paper discusses the mobility of PMs having independent screw-type terminal constraints by introducing the principal screws. Firstly, taking a 3-CCR (C: cylindrical joint, R: revolute joint) PM as an example, the problem of identifying the mobility of PMs having screw-type constraints is proposed. Secondly, combined with the analytical expression of the terminal constraint and theory of quadratic curve decomposition, the mobility determination approach is given. Finally, a numerical example for solving the principal screws and determining the mobility of the 3-CCR PM is provided. Furthermore, the axodes of four poses with three helical DOFs and four poses with three rotational DOFs were plotted. The results show that there is a special phenomenon in which three rotational DOFs and three helical DOFs exist alternately in the workspace of this PM. This paper provides a method for directly identifying the independent helical DOFs in parallel manipulators and for studying the distribution of helical DOFs within the workspace.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Robotic Mechanisms and Dynamics · Soft Robotics and Applications · Robot Manipulation and Learning
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
School of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, China
Hebei Provincial Key Laboratory of Parallel Robot and Mechatronic System, Yanshan University, Qinhuangdao 066004, China
Funding
National Natural Science Foundation of China
References (40)
Show source-provided references
1. Huang, Z., Li, Q.C., and Ding, H.F. (2013). Theory of Parallel Mechanisms, Springer.10.1007/978-94-007-4201-7 ↗
2. Non-overconstrained 3-Dof spherical parallel manipulators of type:: 3-RCC, 3-CCR, 3-CRC10.1017/S0263574705001827 ↗
3. Dynamics modelling and control of the 3-rcc translational platform10.1016/j.mechatronics.2006.06.001 ↗
4. Clearance and manufacturing errors’ effects on the accuracy of the 3-RCC spherical parallel manipulator10.1016/j.euromechsol.2012.05.009 ↗
5. Screw-system-based mobility analysis of a family of fully translational parallel manipulators
6. Position and orientation characteristics of robot mechanisms based on geometric algebra10.1016/j.mechmachtheory.2016.11.001 ↗
7. Ma, T., Bi, F.R., Wang, X., Wang, J., and Pang, G.J. (2020, January 13–15). Development of a new seating platform based on the 3-RCC parallel mechanism. Proceedings of the 5th International Conference on Information Science, Computer Technology and Transportation (ISCTT), Shenyang, China.10.1109/ISCTT51595.2020.00129 ↗
8. Huang, Z., Liu, J., and Li, Y. (2011). On the Degree of Freedom-the General Formula of the Degree of Freedom Which Has Been Searched for 150 Years, Science Press.
9. General methodology for type synthesis of symmetrical lower-mobility parallel manipulators and several novel manipulators10.1177/027836402760475342 ↗
10. The constraint analysis of mechanisms10.1016/0022-2569(66)90016-4 ↗
11. Instantaneous mobility analysis using the twist space intersection approach for parallel mechanism10.1016/j.mechmachtheory.2020.103866 ↗
12. Mobility and constraint analysis of interconnected hybrid flexure systems via screw algebra and graph theory10.1115/1.4035993 ↗
13. Yu, J.J., Pei, X., and Zong, G.H. (2014). Graphical Approach to Creative Design of Mechanical Devices, Beijing Science Press.
14. The lie group of rigid body displacements, a fundamental tool for mechanism design10.1016/S0094-114X(98)00051-2 ↗
15. Lie algebra and the mobility of kinematic chains10.1002/rob.10099 ↗
16. On the determination of the degree of freedom of simple and complex kinematic chains
17. Yang, T.L., and Sun, D.J. (2008, January 3–6). A general formula of degree of freedom for parallel mechanisms. Proceedings of the ASME 2008 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Brooklyn, NY, USA.
18. A geometric algebra approach to determine motion/constraint, mobility and singularity of parallel mechanism10.1016/j.mechmachtheory.2017.06.005 ↗
19. Mobility analysis of limited-degrees-of-freedom parallel mechanisms in the framework of geometric algebra10.1115/1.4032210 ↗
20. Computer-aided mobility analysis of parallel mechanisms10.1016/j.mechmachtheory.2020.103810 ↗
21. An approach for mobility and force/motion transmissibility analysis of parallel mechanisms based on screw theory and CAD technolog10.1177/16878140211050736 ↗
22. A machine learning-based approach for automatic motion/constraint and mobility analysis of parallel robots10.1017/S0263574724000808 ↗
23. Geometry of screw systems—1 screws: Genesis and geometry10.1016/0094-114X(90)90103-Q ↗
24. Geometry of screw systems—2 classification of screw systems10.1016/0094-114X(90)90104-R ↗
25. On the special bases of two- and three-screw systems10.1115/1.2919223 ↗
26. Identification of principal screws of 3-DOF parallel manipulator by quadratic degeneration10.1016/S0094-114X(01)00036-2 ↗
27. Analysis of instantaneous motions of deficient-rank 3-RPS parallel manipulators10.1016/S0094-114X(01)00075-1 ↗
28. Classification of screw systems—I. One- and two-systems10.1016/0094-114X(92)90037-I ↗
29. A general method for the computation of the canonical form of three-systems of infinitesimal screws10.1017/S0263574798000137 ↗
30. Parkin, I.A. (1997, January 14–17). Finding the principal axes of screw systems. Proceedings of the DETC′97 1997 ASME Design Engineering Technical Conferences, Sacramento, CA, USA.
31. Analytical determination of principal twists in serial, parallel and hybrid manipulators using dual vectors and matrices10.1016/j.mechmachtheory.2004.05.017 ↗
32. An eigenproblem approach to classical screw theory10.1016/j.mechmachtheory.2008.07.006 ↗
33. Computational kinematics for robotic manipulators: Instantaneous motion pattern10.1108/02644401011044595 ↗
34. Analytical determination of the principal screws for general screw systems10.1016/j.mechmachtheory.2012.09.008 ↗
35. On the kinematic geometry of relative screw motions10.1007/s12206-012-0624-z ↗
36. Identification of canonical basis of screw systems using general-special decomposition10.1115/1.4039218 ↗
37. Numerical determination of freedom spaces from any set of twists10.1016/j.mechmachtheory.2023.105255 ↗
38. Type synthesis of serial kinematic chains with screw type terminal constraints based on an adding joint method10.1016/j.mechmachtheory.2023.105277 ↗
39. Synthesis of precision serial flexure systems using freedom and constraint topologies (FACT)10.1016/j.precisioneng.2011.04.006 ↗
40. Feasible instantaneous motions and kinematic characteristics of a special 3-DOF 3-UPU parallel manipulator10.1016/j.mechmachtheory.2004.04.004 ↗