Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-10T17:08:07.191Z Has data issue: false hasContentIssue false
  • English
  • Français

Kinematic and Kinetostatic Analysis of Parallel Manipulators with Emphasis on Position, Motion, and Actuation Singularities

Published online by Cambridge University Press:  21 November 2018

M. Kemal Ozgoren
M. Kemal Ozgoren*
Affiliation:
Mechanical Engineering Department, Middle East Technical University, Ankara, Turkey
*
*Corresponding author. E-mail: ozgoren@metu.edu.tr
Get access Rights & Permissions [Opens in a new window]

Summary

This paper provides a contribution to the singularity analysis of the parallel manipulators by introducing the position singularities in addition to the motion and actuation singularities. The motion singularities are associated with the linear velocity mapping between the task and joint spaces. So, they are the singularities of the relevant Jacobian matrices. On the other hand, the position singularities are associated with the nonlinear position mapping between the task and joint spaces. So, they are encountered in the position-level solutions of the forward and inverse kinematics problems. In other words, they come out irrespective of the velocity mapping and the Jacobian matrices. Considering these distinctions, a kinematic singularity is denoted here by one of the four acronyms, which are PSFK (position singularity of forward kinematics), PSIK (position singularity of inverse kinematics), MSFK (motion singularity of forward kinematics), and MSIK (motion singularity of inverse kinematics). There may also occur an actuation singularity (ACTS) concerning the kinetostatic relationships that involve forces and moments. However, it is verified that an ACTS is the same as an MSFK. Each singularity induces different consequences in the joint and task spaces. A PSFK imposes a constraint on the active joint variables and makes the end-effector position indefinite and uncontrollable. Therefore, it must be avoided. An MSFK imposes a constraint on the rates of the active joint variables and makes the end-effector motion indefinite and easily perturbable. Besides, since it is also an ACTS, it causes the actuator torques or forces to grow without bound. Therefore, it must also be avoided. On the other hand, a PSIK imposes a constraint on the end-effector position but provides freedom for the active joint variables. Similarly, an MSIK imposes a constraint on the end-effector motion but provides freedom for the rates of the active joint variables. A PSIK or MSIK need not be avoided if the constraint it imposes on the position or motion of the end-effector is acceptable or if the task can be planned to be compatible with that constraint. Besides, with such a compatible task, a PSIK or MSIK may even be advantageous, because the freedom it provides for the active joint variables can sometimes be used for a secondary purpose. This paper is also concerned with the multiplicities of forward kinematics in the assembly modes of the manipulator and the multiplicities of inverse kinematics in the posture modes of the legs. It is shown that the assembly mode changing poses of the manipulator are the same as the MSFK poses, and the posture mode changing poses of the legs are the same as the MSIK poses.

Keywords

Parallel manipulatorsKinematic analysisPosition analysisVelocity analysisKinetostatic analysisSingularity analysisPosition singularitiesMotion singularitiesActuation singularitiesAssembly modesPosture modes
Type
Articles
Information
Robotica , Volume 37 , Issue 4 , April 2019 , pp. 599 - 625
Copyright
Copyright © Cambridge University Press 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Merlet, J. P., “Singular configurations of parallel manipulators and Grassmann geometry,” IJJR 8, 45–56 (1989).Google Scholar
Gosselin, C. and Angeles, J., “Singularity analysis of closed-loop kinematic chains,” IEEE Trans. Robot. Autom. 6(3), 281–290 (1990).10.1109/70.56660CrossRefGoogle Scholar
Tsai, L. W., Robot Analysis: The Mechanics of Serial and Parallel Manipulators, Ch. 5 (John Wiley and Sons, New York, 1999).Google Scholar
Zlatanov, D., Fenton, R. G. and Benhabib, B., “Identification and classification of the singular configurations of mechanisms,” MMT 33(6), 743–760 (1998).Google Scholar
Park, F. C. and Kim, J. W., “Singularity analysis of closed kinematic chains,” ASME 121, 32–38 (1999).10.1115/1.2829426CrossRefGoogle Scholar
Liu, G., Lou, Y. and Li, Z., “Singularities of parallel manipulators: A geometric treatment,” IEEE Trans. Robot. Autom. 19(4), 579–594 (2003).Google Scholar
Zlatanov, D., Bonev, I. and Gosselin, C., “Constraint singularities as configuration space singularities,” In: Advances in Robot Kinematics (Thomas, F. and Lenarcic, J., eds.) (Springer, Dordrecht, 2002), pp. 183–192.10.1007/978-94-017-0657-5_20CrossRefGoogle Scholar
Bandyopadhyay, S. and Ghosal, A., “Analysis of configuration space singularities of closed-loop mechanisms and parallel manipulators,” MMT 39, 519–544 (2004).Google Scholar
Gregorio, R. D., “Forward problem singularities in parallel manipulators which generate SX-YS-ZS structures,” MMT 40, 600–612 (2004).Google Scholar
Firmani, F. and Podhorodeski, R. P., “Singularity analysis of planar parallel manipulators based on forward kinematic solutions,” MMT 44, 1386–1399 (2009).Google Scholar
Conconi, M. and Carricato, M., “A new assessment of singularities of parallel kinematic chains,” IEEE Trans. Robot. 25(4), 757–770 (2009).10.1109/TRO.2009.2020353CrossRefGoogle Scholar
Liu, S., Qiu, Z. and Zhang, X., “Singularity and path-planning with the working mode conversion of a 3-DOF 3-RRR planar parallel manipulator,” MMT 107, 166–182 (2017).Google Scholar
Hunt, K. H., “Structural kinematics of in-parallel-actuated robot-arms,” ASME Mech. Trans. Autom. Des. 105, 705–712 (1983).10.1115/1.3258540CrossRefGoogle Scholar
Merlet, J.-P., “Direct kinematics and assembly modes of parallel manipulators,” IJJR 11, 150–162 (1992).Google Scholar
Merlet, J.-P., “Direct kinematics of parallel manipulators,” IEEE Trans. Robot. Autom. 9(6), 842–846 (1993).10.1109/70.265928CrossRefGoogle Scholar
Notash, L. and Podhorodeski, R. P., “On the forward displacement problem of three-branch parallel manipulators,” MMT 30(3), 391–404 (1995).Google Scholar
Kong, X. and Gosselin, C. M., “Forward displacement analysis of third-class analytic 3-RPR planar parallel manipulators,” MMT 36, 1009–1018 (2001).Google Scholar
Gan, D., Liao, Q., Dai, J. S., Wei, S. and Seneviratne, L. D., “Forward displacement analysis of the general 6-6 Stewart mechanism using Gröbner bases,” MMT 44, 1640–1647 (2009).Google Scholar
Huang, X., Liao, Q. and Wei, S., “Closed-form forward kinematics for a symmetrical 6-6 Stewart platform using algebraic elimination,” MMT 45, 327–334 (2010).Google Scholar
Gallardo-Alvarado, J., “A simple method to solve the forward displacement analysis of the general six-legged parallel manipulator,” Rob. Comput.-Integr. Manuf. 30, 55–61 (2014).10.1016/j.rcim.2013.09.001CrossRefGoogle Scholar
Wei, F., Wei, S., Zhang, Y. and Liao, Q., “Algebraic solution for the forward displacement analysis of the general 6-6 Stewart mechanism,” Chin. J. Mech. Eng. 29(1), 56–62 (2016).10.3901/CJME.2015.1015.122CrossRefGoogle Scholar
Shen, C., Hang, L. and Yang, T., “Position and orientation characteristics of robot mechanisms based on geometric algebra,” MMT 108, 231–243 (2017).Google Scholar
Ozgoren, M. K., “Kinematic analysis of a manipulator with its position and velocity related singular configurations,” J. Mech. Mach. Theory 34, 1075–1101 (1999).10.1016/S0094-114X(98)00062-7CrossRefGoogle Scholar
Ozgoren, M. K., “Topological analysis of six-joint serial manipulators and their inverse kinematic solutions,” J. Mech. Mach. Theory 37, 511–547 (2002).10.1016/S0094-114X(02)00005-8CrossRefGoogle Scholar
Ozgoren, M. K., “Optimal inverse kinematic solutions for redundant manipulators by using analytical methods to minimize position and velocity measures,” J. Mech. Robot. ASME 5, 031009:1–16 (2013).10.1115/1.4024294CrossRefGoogle Scholar
Hubert, J. and Merlet, J. P., “Singularity analysis through static analysis,” In: Advances in Robot Kinematics: Analysis and Design (Lenarcic, J. and Wenger, P., eds.) (Springer, Dordrecht, 2008).Google Scholar
Briot, S. and Arakelian, V., “Optimal force generation in parallel manipulators for passing through the singular positions,” Int. J. Robot. Res. 27(8), 967–983 (2008).10.1177/0278364908094403CrossRefGoogle Scholar