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Frontiers of Mechanical Engineering

ISSN 2095-0233

ISSN 2095-0241(Online)

CN 11-5984/TH

邮发代号 80-975

2019 Impact Factor: 2.448

Frontiers of Mechanical Engineering  2012, Vol. 7 Issue (2): 120-134   https://doi.org/10.1007/s11465-012-0321-8
  本期目录
Influence of kinematic redundancy on the singularity-free workspace of parallel kinematic machines
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.

Key wordsparallel robots    kinematic redundancy    singularity avoidance    operational workspace
收稿日期: 2012-01-03      出版日期: 2012-06-05
Corresponding Author(s): KOTLARSKI Jens,Email:jens.kotlarski@imes.uni-hannover.de   
 引用本文:   
. Influence of kinematic redundancy on the singularity-free workspace of parallel kinematic machines[J]. Frontiers of Mechanical Engineering, 2012, 7(2): 120-134.
Jens KOTLARSKI, Bodo HEIMANN, Tobias ORTMAIER. Influence of kinematic redundancy on the singularity-free workspace of parallel kinematic machines. Front. Mech. Eng., 2012, 7(2): 120-134.
 链接本文:  
https://academic.hep.com.cn/fme/CN/10.1007/s11465-012-0321-8
https://academic.hep.com.cn/fme/CN/Y2012/V7/I2/120
Fig.1  
Fig.2  
Fig.3  
Fig.4  
Fig.5  
i=1i=2i=3
?(0)xGi/m0.601.2
?(0)yGi/m27/500
?(E)xPi/m0-0.1250.125
?(E)yPi/m0-3/8-3/8
l1,i/m0.60.60.6
l2,i/m0.60.60.6
Tab.1  
Fig.6  
EE orientation αE
-60°-30°30°60°
?ηi=(wi,red-wi,nred)/wi,nred/%
3(P)RRR?ηa7.56.96.06.97.5
?ηo15.621.321.27.141.3
Tab.2  
Fig.7  
Fig.8  
i=1i=2i=3
?(0)xGi/m0.601.2
?(0)yGi/m27/500
?(E)xPi/m0–0.1250.125
?(E)yPi/m0-3/8-3/8
ρmin?,i/m0.10.10.1
ρmax?,i/m1.21.21.2
Tab.3  
Fig.9  
EE orientation αE
-60°-30°30°60°
Δηi=(wi,red-wi,nred)/wi,nred
3(P)RPR?ηa11.09.78.59.611.0
?ηo5.826.126.15.8
Tab.4  
Fig.10  
i=1i=2i=3i=4i=5i=6
?(0)xGi/m-bsπbsπbsπ bsπ bsπ bsπ
?(0)yGi/mbcπbcπbcπ bcπ bcπ bcπ
?(0)zGi/m000000
?(E)xPi/m-psπ psπ psπ psπpsπpsπ
?(E)yPi/mpcπ pcπ pcπ pcπpcπpcπ
?(E)zPi/m000000
ρmin?,i/m0.390.390.390.390.390.39
ρmax?,i/m0.950.950.950.950.950.95
Tab.5  
Fig.11  
EE orientation aE=βE=γΕφE
-60°-30°30°60°
?ηi=(wi,red-wi,nred)/wi,nred/%
6(R)UPS?ηa12.012.59.711.412.0
?ηo434.433.79.458.338.8
Tab.6  
Fig.12  
i=1i=2i=3i=4i=5i=6
?(0)xGim-bsπ bsπ bsπ bsπ bsπ bsπ
?(0)yGimbcπ bcπ bcπ bcπ bcπ bcπ
?(0)zGim000000
?(E)xPim-psπ psπ psπ psπpsπ psπ
?(E)yPimpcπ pcπ pcπ pcπpcπ pcπ
?(E)xPim000000
li,1 m0.240.240.240.240.240.24
li,2 m0.560.560.560.560.560.56
Tab.7  
Fig.13  
EE orientation aE=βE=γΕφE
-60°-30°30°60°
?ηi=(wi,red-wi,nred)/wi,nred/%
6(R)RUS?ηa10.16.53.19.712.2
?ηo130.53.1197.250.2
Tab.8  
Fig.14  
EE orientation aE=(βE=γEφE)
-60°-30°30°60°
?ηi=(wi,red-wi,nred)/wi,nred/%
3(P)RRR?ηa7.56.96.06.97.5
?ηo15.621.321.27.141.3
3(P) RPR?ηa11.09.78.59.611.0
?ηo5.826.126.15.8
6(P) UPS?ηa12.012.59.711.412.0
?ηo434.433.79.458.338.8
6(P) RUS?ηa10.16.53.19.712.2
?ηo130.53.1197.250.2
Tab.9  
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