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Frontiers of Mechanical Engineering

ISSN 2095-0233

ISSN 2095-0241(Online)

CN 11-5984/TH

Postal Subscription Code 80-975

2018 Impact Factor: 0.989

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Front. Mech. Eng.    2018, Vol. 13 Issue (3) : 368-375    https://doi.org/10.1007/s11465-018-0519-5
RESEARCH ARTICLE
Fast forward kinematics algorithm for real-time and high-precision control of the 3-RPS parallel mechanism
Yue WANG1, Jingjun YU1(), Xu PEI2
1. Robotics Institute, Beihang University, Beijing 100191, China
2. Department of Mechanical Design, Beihang University, Beijing 100191, China
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Abstract

A new forward kinematics algorithm for the mechanism of 3-RPS (R: Revolute; P: Prismatic; S: Spherical) parallel manipulators is proposed in this study. This algorithm is primarily based on the special geometric conditions of the 3-RPS parallel mechanism, and it eliminates the errors produced by parasitic motions to improve and ensure accuracy. Specifically, the errors can be less than 10−6. In this method, only the group of solutions that is consistent with the actual situation of the platform is obtained rapidly. This algorithm substantially improves calculation efficiency because the selected initial values are reasonable, and all the formulas in the calculation are analytical. This novel forward kinematics algorithm is well suited for real-time and high-precision control of the 3-RPS parallel mechanism.
Keywords 3-RPS parallel mechanism      forward kinematics      numerical algorithm      parasitic motion     
Corresponding Author(s): Jingjun YU   
Just Accepted Date: 10 May 2018   Online First Date: 01 June 2018    Issue Date: 11 June 2018
 Cite this article:   
Yue WANG,Jingjun YU,Xu PEI. Fast forward kinematics algorithm for real-time and high-precision control of the 3-RPS parallel mechanism[J]. Front. Mech. Eng., 2018, 13(3): 368-375.
 URL:  
https://academic.hep.com.cn/fme/EN/10.1007/s11465-018-0519-5
https://academic.hep.com.cn/fme/EN/Y2018/V13/I3/368
Fig.1  3-RPS parallel mechanism
Fig.2  Quadrilateral formed by branch Aa
Fig.3  Flow diagram of the proposed forward kinematics algorithm
Group a/(° ) b/(° ) Z/mm Length of Aa/mm Length of Bb/mm Length of Cc/mm
1 16.400 9.100 106.540 91.897081 123.295676 138.546005
2 100.250 3.480 129.478 140.061386 123.614806 146.892508
3 235.486 7.256 146.210 167.611093 164.189018 131.095900
4 324.900 4.800 175.364 168.815269 196.694571 180.289988
5 90.000 5.000 190.000 195.876527 181.573991 210.812560
6 37.400 8.400 210.895 194.137285 212.397102 243.187208
7 164.250 4.480 234.560 254.326640 228.536706 235.607788
8 252.394 6.295 250.000 261.013313 269.189400 233.921769
9 335.900 1.200 264.358 264.928866 272.025620 269.100274
10 180.000 6.000 286.186 311.078411 279.879924 279.879924
11 82.400 8.700 304.320 303.963635 284.729504 336.147716
12 137.610 2.840 333.310 344.014466 327.450265 338.838962
13 294.351 5.281 360.250 355.893204 381.759734 352.822726
14 351.900 9.500 379.420 350.618093 402.745397 394.588460
15 270.000 4.000 395.000 397.876456 409.959639 385.975476
Tab.1  Selected input parameters and results of inverse kinematics
Group Calculated a/(° ) Calculated b/(° ) Calculated Z/mm Errors of a/(° ) Errors of b/(° ) Errors of Z/mm
1 16.399999990319 9.100000015514 106.539999824347 9.68100 × 10−9 1.5514 × 10−8 1.75653 × 10−7
2 100.250000123126 3.480000012915 129.477999826060 1.23126 × 10−7 1.2915 × 10−8 1.73940 × 10−7
3 235.485999591757 7.256000014810 146.209999826362 4.08243 × 10−7 1.4810 × 10−8 1.73638 × 10−7
4 324.899999626901 4.800000013587 175.363999826754 3.73099 × 10−7 1.3587 × 10−8 1.73246 × 10−7
5 90.000000034505 5.000000017007 189.999999826339 3.4505 0× 10−8 1.7007 × 10−8 1.73661 × 10−7
6 37.399999884469 8.400000034160 210.894999823250 1.15531 × 10−7 3.4160 × 10−8 1.76750 × 10−7
7 164.249999997588 4.480000017985 234.559999826719 2.41200 × 10−9 1.7985 × 10−8 1.73281 × 10−7
8 252.393999580079 6.295000030069 249.999999825171 4.19921 × 10−7 3.0069 × 10−8 1.74829 × 10−7
9 335.899999589428 1.200000005785 264.357999827608 4.10572 × 10−9 5.7850 × 10−9 1.72392 × 10−7
10 180.000000205680 6.000000024986 286.185999826681 2.05680 × 10−7 2.4986 × 10−8 1.73319 × 10−7
11 82.400000007047 8.700000046823 304.319999823693 7.04700 × 10−9 4.6832 × 10−8 1.76307 × 10−7
12 137.609999996813 2.840000018076 333.309999827179 3.18700 × 10−9 1.8076 × 10−8 1.72821 × 10−7
13 294.350999585253 5.281000033633 360.249999826221 4.14747 × 10−7 3.3633 × 10−8 1.73779 × 10−7
14 351.899999593787 9.500000066769 379.419999822330 4.06213 × 10−7 6.6769 × 10−7 1.77670 × 10−7
15 269.999999583588 4.000000029386 394.999999826735 4.16412 × 10−7 2.9386 × 10−9 1.73265 × 10−7
Tab.2  Results calculated by the proposed forward kinematics algorithm and its errors
Group Time/µs
1 81.918557
3 62.942773
6 46.681530
10 32.225315
13 35.839369
Tab.3  Calculation time
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[1] Haibo QU, Yuefa FANG, Sheng GUO. Parasitic rotation evaluation and avoidance of 3-UPU parallel mechanism[J]. Front Mech Eng, 2012, 7(2): 210-218.
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