Influence of kinematic redundancy on the singularity-free workspace of parallel kinematic machines

doi:10.1007/s11465-012-0321-8

Front. Mech. Eng.

2012, Vol. 7

Issue (2) : 120-134 https://doi.org/10.1007/s11465-012-0321-8

RESEARCH ARTICLE

Influence of kinematic redundancy on the singularity-free workspace of parallel kinematic machines

Jens KOTLARSKI(

), Bodo HEIMANN, Tobias ORTMAIER

Institute of Mechatronic Systems, Leibniz Universität Hannover, 30167 Hanover, Germany

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Abstract

In this paper the effect of kinematic redundancy in order to reduce the singularity loci of the direct kinematics and to increase the operational, i.e., singularity-free, workspace is demonstrated. The proposed approach consists of additional prismatic actuators allowing one or more base joints to move linearly. As a result, a selective reconfiguration can be performed in order to avoid singular configurations. Exemplarily, kinematically redundant schemes of four structures, the 3RRR, the 3RPR, the 6UPS, and the 6RUS, are considered. The relationship between the redundancy and the operational workspace is studied and several analysis examples demonstrate the effectiveness of the proposed concept. Furthermore, the additional benefit of an increasing number of redundant actuators is discussed.

Keywords parallel robots kinematic redundancy singularity avoidance operational workspace

Corresponding Author(s): KOTLARSKI Jens,Email:jens.kotlarski@imes.uni-hannover.de

Issue Date: 05 June 2012

Cite this article:

Jens KOTLARSKI,Bodo HEIMANN,Tobias ORTMAIER. Influence of kinematic redundancy on the singularity-free workspace of parallel kinematic machines[J]. Front. Mech. Eng., 2012, 7(2): 120-134.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-012-0321-8
https://academic.hep.com.cn/fme/EN/Y2012/V7/I2/120

Fig.1 Workspace reduction due to an additional kinematic chain, exemplarily demonstrated for a planar mechanism with revolute actuators. (a) Non-redundant 3RRR; (b) redundant 4RRR

Fig.2 Variation of the singularity loci within the overall workspace due to the redundant actuator configuration, i.e., the base joint position; top: redundant 3(P)RRR, bottom: redundant 3(P)RPR

Fig.3 Trajectory (bold line) going through a singular configuration, a reconfiguration (from the left to the right) allows to follow the desired path

Fig.4 Areas of equal signs of det () within the workspace

Fig.5 Kinematically redundant 3(P)RRR mechanism

Tab.1 Design parameters of the analyzed 3(P)RRR mechanism

Fig.6 Overall (bold lines and circles, respectively) and operational (light lines and dots, respectively) of the redundant 3(P)RRR mechanism (red) and its non-redundant counterpart (blue). (a) =-60°; (b) =-30°; (c) =0°; (d) =30°; (e) =60°

Tab.2 Results of the performed workspace analysis of the 3RRR-based mechanism

Fig.7 Areas of equal signs of det() within the workspace; the blank part represents the area with det()<0 and the red part the area with det()>0.(a)Non-redundant 3RRR;(b)redundant 3(P)RRR

Fig.8 Kinematically redundant 3(P)RPR mechanism. (a) =-60°; (b) =-30°; (c) =0°; (d) =30°; (e) =60°

Tab.3 Design parameters of the analyzed 3(P)RPR mechanism

Fig.9 Overall (bold lines and circles, respectively) and operational (light lines and dots, respectively) of the redundant 3(P)RPR mechanism (red) and its non-redundant counterpart (blue). (a) =-60°; (b) =-30°; (c) =0°; (d) =30°; (e) =60°

Tab.4 Results of the performed workspace analysis of the 3RPR-based mechanism

Fig.10 Kinematically redundant 6(P)UPS mechanism

Tab.5 Design parameters of the analyzed 6(P)UPS mechanism, = 0.43 m and = 0.09 m

Fig.11 Overall (bold lines and circles, respectively) and operational (light lines and dots, respectively) of the redundant 6(P)UPS mechanism (red) and its non-redundant counterpart (blue); . (a) =-60°; (b) =-30°; (c) =0°; (d) =30°; (e) =60°

Tab.6 Results of the performed workspace analysis of the 6UPS-based mechanism

Fig.12 Kinematically redundant 6(P)RUS mechanism

Tab.7 Design parameters of the analyzed 6(P)RUS mechanism, = 0.364 m and = 0.073 m

Fig.13 Overall (bold lines and circles, respectively) and operational (light lines and dots, respectively) of the redundant 6(P)RUS mechanism (red) and its non-redundant counterpart (blue);

Tab.8 Results of the performed workspace analysis of the 6RUS-based mechanism

Fig.14 Workspace sizes (lines) and (circles) with respect to the number of redundant actuators for all the considered mechanism. (a) 3(P)RRR; (b) 3(P)RPR; (c) 6(P)UPS; (d) 6(P)RUS

Tab.9 Summarized results of the performed workspace analysis

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