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

Date

2019-04-01

Author

Özgören, Mustafa Kemal

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

147
views

0
downloads

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.

Subject Keywords

Parallel manipulators, Kinematic analysis, Position analysis, Velocity analysis, Kinetostatic analysis, Singularity analysis, Position singularities, Motion singularities, Actuation singularities, Assembly modes, Posture modes

URI

https://hdl.handle.net/11511/31597

Journal

ROBOTICA

DOI

https://doi.org/10.1017/s0263574718001194

Collections

Graduate School of Natural and Applied Sciences, Article

Suggestions

OpenMETU
Core

Kinematic analysis of spatial mechanical systems using exponential rotation matrices Özgören, Mustafa Kemal (2007-11-01) The mathematical properties associated with the exponential rotation matrices are reviewed. By means of two typical mechanism examples, it is demonstrated that these properties constitute a versatile analytical tool, which can be used eftectively in kinematic studies on spatial mechanical systems involving position, velocity, acceleration, and singularity analyses.
Integral criteria for oscillation of third order nonlinear differential equations AKTAŞ, MUSTAFA FAHRİ; Tiryaki, Aydın; Zafer, Ağacık (Elsevier BV, 2009-12-15) In this paper we are concerned with the oscillation of third order nonlinear differential equations of the form
Kinematic and force analyses of overconstrained mechanisms Üstün, Deniz; Özgören, Mustafa Kemal; Department of Mechanical Engineering (2011) This thesis comprises a study on the kinematic and force analyses of the overconstrained mechanisms. The scope of the overconstrained mechanisms is too wide and difficult to handle. Therefore, the study is restricted to the planar overconstrained mechanisms. Although the study involves only the planar overconstrained mechanisms, the investigated methods and approaches could be extended to the spatial overconstrained mechanisms as well. In this thesis, kinematic analysis is performed in order to investigate ...
Kinematic analysis of a manipulator with its position and velocity related singular configurations Özgören, Mustafa Kemal (1999-10-01) Forward and inverse kinematic analyses of a generic 6-R serial manipulator are carried out at both position and velocity levels. Singular configurations associated with the inverse position solution, designated as position related singular configurations (POSCs), and those associated with the inverse velocity solution, designated as velocity related singular configurations (VESOs), are investigated. At POSCs, the specified pose of the hand is not sufficient to determine some of the joint variables; the moti...
Modal analysis of elastic vibrations of incompressible materials using a pressure-stabilized finite element method Codina, Ramon; Türk, Önder (2022-09-01) This paper describes a modal analysis technique to approximate the vibrations of incompressible elastic solids using a stabilized finite element method to approximate the associated eigenvalue problem. It is explained why residual based formulations are not appropriate in this case, and a formulation involving only the pressure gradient is employed. The effect of the stabilization term compared to a Galerkin approach is detailed, both in the derivation of the approximate formulation and in the error estimat...

Citation Formats

M. K. Özgören, “Kinematic and Kinetostatic Analysis of Parallel Manipulators with Emphasis on Position, Motion, and Actuation Singularities,” ROBOTICA, pp. 599–625, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/31597.