Position, Jacobian, decoupling and workspace analysis of a novel parallel manipulator with four pneumatic artificial muscles

  • Wanshun Zang
  • Kejiang Zang
  • Gang ShenEmail author
  • Xiang Li
  • Ge Li
Technical Paper


This paper firstly presents a novel 4-SPS/S (active chain/passive chain) parallel manipulator (PPM) driven by four pneumatic artificial muscles (PAMs). SPS denotes a spherical pair–prismatic pair–spherical pair chain and S denotes a spherical pair chain. The PPM proposed can be utilized as shoulder, wrist, waist, hip and ankle simulators or ankle rehabilitation robot. And we present a comprehensive analysis on the PPM proposed, including degrees of freedom (DOF), position, kinematic, Jacobian, singularity, decoupling and workspace analysis. In order to decrease the influence of the maximum angle of spherical pairs in four active chains on the workspace, a novel connector for PAM is proposed. The structure of the PPM is explicitly described, and DOF of the PPM are analyzed based on constraint screw theory. The posture of the moving platform (MP) of the PPM is obtained though ZYX (αβγ) type Euler angles and the inverse position solution is obtained. When the MP moves toward any a single Euler angle direction, the closed-form direct position solution is presented by geometric analysis. A back propagation (BP) neural network model for the whole direct position solution is established. Two methods for the Jacobian matrix, one velocity composition, one differentiation, are addressed, and the acceleration inversion is obtained. Based on the Jacobian matrix, the singularity and kinematic decoupling of the PPM are both analyzed. The geometric model of expanded PAM is introduced, and the change of diameters of four PAMs in active chains is taken into consideration when chains of the PPM interfere. Based on length ranges of four active chains, the maximum angle of spherical pairs and possible interferences between chains of the PPM, the configuration workspace is presented. Finally, the characteristic of the workspace and the influence of the maximum angle of spherical pairs in active chains on the configuration workspace are both analyzed.


Novel parallel manipulator Pneumatic artificial muscle Kinematic analysis Jacobian matrix Singularity Decoupling Workspace 



This research was supported by the National Natural Science Foundation of China (No. 51575511) and the Longyan University Doctoral Foundation funded project (LB2018035).


  1. 1.
    Minh TV, Kamers B, Ramon H, Van Brussel H (2012) Modeling and control of a pneumatic artificial muscle manipulator joint-part I: modeling of a pneumatic artificial muscle manipulator joint with accounting for creep effect. Mechatronics 22(7):923–933Google Scholar
  2. 2.
    Choi TY, Choi BS, Seo KH (2011) Position and compliance control of a pneumatic muscle actuated manipulator for enhanced safety. IEEE Trans Control Syst Technol 19(4):832–842Google Scholar
  3. 3.
    Zhu X, Tao G, Yao B, Cao J (2008) Adaptive robust posture control of a parallel manipulator driven by pneumatic muscles. Automatica 44(9):2248–2257MathSciNetzbMATHGoogle Scholar
  4. 4.
    Park YL, Chen BR, Pérez-Arancibia NO, Young D, Stirling L, Wood RJ, Nagpal R (2014) Design and control of a bio-inspired soft wearable robotic device for ankle–foot rehabilitation. Bioinspir Biomim 9(1):016007Google Scholar
  5. 5.
    Chou CP, Hannaford B (1996) Measurement and modeling of McKibben pneumatic artificial muscles. IEEE Trans Robot Autom 12(1):90–102Google Scholar
  6. 6.
    Tondu B, Boitier V, Lopez P (1994, October) Naturally compliant robot-arms actuated by McKibben artificial muscles. In: 1994 IEEE international conference on systems, man, and cybernetics, 1994. Humans, information and technology, vol 3. IEEE, pp 2635–2640Google Scholar
  7. 7.
    Minh TV, Tjahjowidodo T, Ramon H, Van Brussel H (2010) Cascade position control of a single pneumatic artificial muscle-mass system with hysteresis compensation. Mechatronics 20(3):402–414Google Scholar
  8. 8.
    Tjahyono AP, Aw KC, Devaraj H, Surendra W, Haemmerle E, Travas-Sejdic J (2013) A five-fingered hand exoskeleton driven by pneumatic artificial muscles with novel polypyrrole sensors. Ind Robot Int J 40(3):251–260Google Scholar
  9. 9.
    Waycaster G, Wu SK, Shen X (2011) Design and control of a pneumatic artificial muscle actuated above-knee prosthesis. J Med Devices 5(3):031003Google Scholar
  10. 10.
    Andrikopoulos G, Nikolakopoulos G, Manesis S (2015) Design and development of an exoskeletal wrist prototype via pneumatic artificial muscles. Meccanica 50(11):2709–2730Google Scholar
  11. 11.
    Zhu X, Tao G, Yao B, Cao J (2008) Adaptive robust posture control of parallel manipulator driven by pneumatic muscles with redundancy. IEEE/ASME Trans Mechatron 13(4):441–450zbMATHGoogle Scholar
  12. 12.
    Shi GL, Shen WEI (2013) Hybrid control of a parallel platform based on pneumatic artificial muscles combining sliding mode controller and adaptive fuzzy CMAC. Control Eng Practice 21(1):76–86Google Scholar
  13. 13.
    Kosaki T, Sano M (2011) Control of a parallel manipulator driven by pneumatic muscle actuators based on a hysteresis model. J Environ Eng 6(2):316–327Google Scholar
  14. 14.
    Truong DQ, Ahn KK (2013) Synchronization controller for a 3-R planar parallel pneumatic artificial muscle (PAM) robot using modified ANFIS algorithm. Mechatronics 23(4):462–479Google Scholar
  15. 15.
    Thanh TDC, Ahn KK (2006) Nonlinear PID control to improve the control performance of 2 axes pneumatic artificial muscle manipulator using neural network. Mechatronics 16(9):577–587Google Scholar
  16. 16.
    Masouleh MT, Gosselin C, Husty M, Walter DR (2011) Forward kinematic problem of 5-RPUR parallel mechanisms (3T2R) with identical limb structures. Mech Mach Theory 46(7):945–959zbMATHGoogle Scholar
  17. 17.
    Innocenti C, Parenti-Castelli V (1993) Closed-form direct position analysis of a 5-5 parallel mechanism. J Mech Des 115(3):515–521zbMATHGoogle Scholar
  18. 18.
    Abbasnejad G, Daniali HM, Fathi A (2012) Closed form solution for direct kinematics of a 4PUS + 1PS parallel manipulator. Sci Iran 19(2):320–326Google Scholar
  19. 19.
    Ruggiu M, Kong X (2012) Mobility and kinematic analysis of a parallel mechanism with both PPR and planar operation modes. Mech Mach Theory 55:77–90Google Scholar
  20. 20.
    Dalvand MM, Shirinzadeh B (2011) Forward kinematics analysis of offset 6-RR C RR parallel manipulators. Proc Inst Mech Eng C J Mech Eng Sci 225(12):3011–3018Google Scholar
  21. 21.
    Shen H, Yin H, Wang Z, Huang T, Li J, Deng J, Yang T (2013) Research on forward position solutions for 6-SPS parallel mechanisms based on topology structure analysis. J Mech Eng 21:010Google Scholar
  22. 22.
    Gosselin C, Angeles J (1990) Singularity analysis of closed-loop kinematic chains. IEEE Trans Robot Autom 6(3):281–290Google Scholar
  23. 23.
    Qazani MRC, Pedrammehr S, Rahmani A, Danaei B, Ettefagh MM, Rajab AKS, Abdi H (2015) Kinematic analysis and workspace determination of hexarot-a novel 6-DOF parallel manipulator with a rotation-symmetric arm system. Robotica 33(8):1686–1703Google Scholar
  24. 24.
    Sadjadian H, Taghirad HD (2006) Kinematic, singularity and stiffness analysis of the hydraulic shoulder: a 3-dof redundant parallel manipulator. Adv Robot 20(7):763–781Google Scholar
  25. 25.
    Rezaei A, Akbarzadeh A, Nia PM, Akbarzadeh-T MR (2013) Position, Jacobian and workspace analysis of a 3-PSP spatial parallel manipulator. Robot Comput Integr Manuf 29(4):158–173Google Scholar
  26. 26.
    Gan D, Dai JS, Dias J, Umer R, Seneviratne L (2015) Singularity-free workspace aimed optimal design of a 2T2R parallel mechanism for automated fiber placement. J Mech Robot 7(4):041022Google Scholar
  27. 27.
    Ruggiu M (2009) Position analysis, workspace, and optimization of a 3-PPS spatial manipulator. J Mech Des 131(5):051010Google Scholar
  28. 28.
    Jin Y, Chen IM, Yang G (2006) Kinematic design of a 6-DOF parallel manipulator with decoupled translation and rotation. IEEE Trans Rob 22(3):545–551Google Scholar
  29. 29.
    Jin Y, Chen IM, Yang G (2009) Kinematic design of a family of 6-DOF partially decoupled parallel manipulators. Mech Mach Theory 44(5):912–922zbMATHGoogle Scholar
  30. 30.
    Ti-Xian T, Hong-Zhou J, Zhi-Zhong T, Jing-Feng H (2015) Modal space decoupled optimal design for a class of symmetric spatial parallel mechanisms with consideration of passive joint damping. Robotica 33(4):828–847Google Scholar
  31. 31.
    Baron L, Angles J (2000) The kinematic decoupling of parallel manipulators using joint-sensor data. IEEE Trans Robot Autom 16(6):644–651Google Scholar
  32. 32.
    Legnani G, Fassi I, Giberti H, Cinquemani S, Tosi D (2012) A new isotropic and decoupled 6-DoF parallel manipulator. Mech Mach Theory 58:64–81zbMATHGoogle Scholar
  33. 33.
    Hao G, Yu J (2016) Design, modelling and analysis of a completely-decoupled XY compliant parallel manipulator. Mech Mach Theory 102:179–195Google Scholar
  34. 34.
    Yang C, Han J (2013) Dynamic coupling analysis of a spatial 6-DOF electro-hydraulic parallel manipulator using a modal decoupling method. Int J Adv Robot Syst 10(2):104Google Scholar
  35. 35.
    Huang Z, Li Q, Ding H (2012) Theory of parallel mechanisms, vol 6. Springer, BerlinGoogle Scholar
  36. 36.
    Benedict CE, Tesar D (1978) Model formulation of complex mechanisms with multiple inputs: part II—the dynamic model. J Mech Des 100(4):755–761Google Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  • Wanshun Zang
    • 1
    • 2
  • Kejiang Zang
    • 3
  • Gang Shen
    • 1
    • 2
    Email author
  • Xiang Li
    • 1
    • 2
  • Ge Li
    • 1
    • 2
  1. 1.School of Mechatronic EngineeringChina University of Mining and TechnologyXuzhouChina
  2. 2.Jiangsu Key Laboratory of Mine Mechanical and Electrical EquipmentChina University of Mining and TechnologyXuzhouChina
  3. 3.School of Physics and Mechanical and Electrical EngineeringLongyan UniversityLongyanChina

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