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New methodology for multi-dimensional spinal joint testing with a parallel robot

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Abstract

Six degree-of-freedom (6DOF) robots can be used to examine joints and their mechanical properties with the spatial freedom encountered physiologically. Parallel robots are capable of 6DOF motion under large payloads making them ideal for joint testing. This study developed and assessed novel methods for spinal joint testing with a custom-built parallel robot implementing hybrid load-position control. We hypothesized these methods would allow multi-dimensional control of joint loading scenarios, resulting in physiological joint motions. Tests were performed in 3DOF and 6DOF. 3DOF methods controlled the forces and the principal moment within ±10 N and 0.25 N m under combined bending and compressive loads. 6DOF tests required larger tolerances for convergence due to machine compliance, however expected motion patterns were still observed. The unique mechanism and control approaches show promise for enabling complex three-dimensional loading patterns for in vitro joint biomechanics, and could facilitate research using specimens with unknown, changing, or nonlinear load-deformation properties.

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Abbreviations

Letter superscripts represent the coordinate system that a variable is expressed in. No superscript denotes that the variable is relative to the global coordinate system.:

 

e:

superscript, end-effector coordinate system

d:

superscript, disc (joint) coordinate system

T:

superscript, matrix transpose

Δ:

change in the value of a variable

⊗:

tensor-product

ℓ:

machine leg length

b :

3 × 1 base plate joint center position

e e :

3 × 1 end-effector joint center position

R :

3 × 3 rotation matrix

t :

3 × 1 translation vector

J −1 :

6 × 6 inverse kinematic Jacobian matrix

X :

6 × 1 end-effector pose matrix (3 translations, 3 rotations)

L :

6 × 1 inverse kinematics calculated leg lengths (ℓ1, ℓ2,...,ℓ6)

L′:

6 × 1 potentiometer measured leg lengths

F d :

6 × 1 joint load matrix (3 forces, 3 moments)

P d :

6 × 1 joint pose matrix

C d :

6 × 6 joint compliance (inverse stiffness) matrix

References

  1. Abbasi WA, Ridgeway SC, Adsit PD et al (2001) Investigation of a special 6–6 parallel platform for contour milling. Centre for Intelligent Machines and Robotics

  2. Adams MA, Hutton WC, Stott JR (1980) The resistance to flexion of the lumbar intervertebral joint. Spine 5:245–253

    Article  Google Scholar 

  3. Broyden CG (1965) A class of methods for solving nonlinear simultaneous equations. Math Comput 19:577–593

    Article  MATH  MathSciNet  Google Scholar 

  4. Cripton PA, Bruehlmann SB, Orr TE et al (2000) In vitro axial preload application during spine flexibility testing: towards reduced apparatus-related artefacts. J Biomech 33:1559–1568

    Article  Google Scholar 

  5. Dasgupta B, Mruthyunjaya TS (2000) The stewart platform manipulator: a review. Mech Mach Theory 35:15–40

    Article  MATH  MathSciNet  Google Scholar 

  6. De Schutter J, Bruyninckx H, Zhu W-H et al (1997) Force control: a bird’s eye view. Presented at the IEEE CSS/RAS international workshop on control problems in robotics and automation: future directions, San Diego

  7. Dickey JP, Gillespie KA (2003) Representation of passive spinal element contributions to in vitro flexion–extension using a polynomial model: illustration using the porcine lumbar spine. J Biomech 36:883–888

    Article  Google Scholar 

  8. Dickey JP, Kerr DJ (2003) Effect of specimen length: are the mechanics of individual motion segments comparable in functional spinal units and multisegment specimens? Med Eng Phys 25:221–227

    Article  Google Scholar 

  9. Fujie H, Mabuchi K, Woo SL et al (1993) The use of robotics technology to study human joint kinematics: a new methodology. J Biomech Eng 115:211–217

    Google Scholar 

  10. Gilbertson LG, Doehring TC, Kang JD (2000) New methods to study lumbar spine biomechanics: delineation of in vitro load-displacement characteristics by using a robotics/UFS testing system with hybrid control. Oper Tech Orthop 10:246–253

    Article  Google Scholar 

  11. Gillespie KA (2002) Biomechanical role of lumbar spine ligaments in flexion and extension using a parallel linkage robot: a porcine model. Masters Thesis, University of Guelph, Guelph

  12. Gillespie KA, Dickey JP (2004) Biomechanical role of lumbar spine ligaments in flexion and extension: determination using a parallel linkage robot and a porcine model. Spine 29(11):1208–1216

    Article  Google Scholar 

  13. Goel VK, Winterbottom JM, Weinstein JN et al (1987) Load sharing among spinal elements of a motion segment in extension and lateral bending. J Biomech Eng 109:291–297

    Article  Google Scholar 

  14. Gorinevsky DM, Formalsky AM, Schneider AY (1997) Force control of robotic systems. CRC Press, Boca Raton

    Google Scholar 

  15. Janevic J, Ashton-Miller JA, Schultz AB (1991) Large compressive preloads decrease lumbar motion segment flexibility. J Orthop Res 9:228–236

    Article  Google Scholar 

  16. Khatib O (1987) A unified approach for motion and force control of robot manipulators: the operational space formulation. J Rob Autom RA-3:43–53

    Article  Google Scholar 

  17. Lee Shee NK, Dickey JP (2005) In vitro testing of knee joints using robotics: computer programming theory. Presented at the XXth Congress of the international society of biomechanics, August 1–5, Cleveland

  18. Li G, DeFrate LE, Zayontz S et al (2004) The effect of tibiofemoral joint kinematics on patellofemoral contact pressures under simulated muscle loads. J Orthop Res 22:801–806

    Article  Google Scholar 

  19. Lysack JT, Dickey JP, Dumas GA et al (2000) A continuous pure moment loading apparatus for biomechanical testing of multi-segment spine specimens. J Biomech 33:765–770

    Article  Google Scholar 

  20. Ma CB, Kanamori A, Vogrin TM et al (2003) Measurement of posterior tibial translation in the posterior cruciate ligament-reconstructed knee: significance of the shift in the reference position. Am J Sports Med 31:843–848

    Google Scholar 

  21. Merlet J-P (1999) Parallel robots. Kluwer, Boston

    Google Scholar 

  22. Most E (2000) Development of a 6-DOF robotic test system for studying the biomechanics of total knee replacement. Masters Thesis, Massachusetts Institute of Technology, Cambridge

  23. Panjabi MM, Oxland TR, Yamamoto I et al (1994) Mechanical behaviour of the human lumbar and lumbosacral spine as shown by three-dimensional load-displacement curves. J Bone Joint Surg (Am) 76:413–424

    Google Scholar 

  24. Pearcy MJ, Tibrewal SB (1984) Axial rotation and lateral bending in the normal lumbar spine measured by three-dimensional radiography. Spine 9:582–587

    Article  Google Scholar 

  25. Schendel MJ, Wood KB, Buttermann GR et al (1993) Experimental measurement of ligament force, facet force, and segment motion in the human lumbar spine. J Biomech 26:427–438

    Article  Google Scholar 

  26. Stewart D (1965) A platform with six degrees of freedom. Proc Inst Mech Eng 180(Pt.1):371–386

    Google Scholar 

  27. Stokes IA, Gardner-Morse M, Churchill D et al (2002) Measurement of a spinal motion segment stiffness matrix. J Biomech 35:517–521

    Article  Google Scholar 

  28. Thompson RE, Barker TM, Pearcy MJ (2003) Defining the neutral zone of sheep intervertebral joints during dynamic motions: an in vitro study. Clin Biomech 18:89–98

    Article  Google Scholar 

  29. Tian L, Gilbertson LG (2004) The study of control methods for the robotic testing system for human musculoskeletal joints. Comput Methods Programs Biomed 74:211–220

    Article  Google Scholar 

  30. Wilke HJ, Claes L, Schmitt H et al (1994) A universal spine tester for in vitro experiments with muscle force simulation. Eur Spine J 3:91–97

    Article  Google Scholar 

  31. Wilke HJ, Wenger K, Claes L (1998) Testing criteria for spinal implants: recommendations for the standardization of in vitro stability testing of spinal implants. Eur Spine J 7:148–154

    Article  Google Scholar 

  32. Woo SL, Debski RE, Wong EK et al (1999) Use of robotic technology for diathrodial joint research. J Sci Med Sport 2:283–297

    Article  Google Scholar 

  33. Zhuang H, Yan J, Masory O (1998) Calibration of stewart platforms and other parallel manipulators by minimizing inverse kinematic residuals. J Rob Syst 15:395–405

    Article  MATH  Google Scholar 

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Acknowledgments

This study was supported by a grant from the Natural Sciences and Engineering Research Council of Canada. The authors thank Dr. Jean-Pierre Merlet for discussions on parallel robot kinematics and control, and Dr. Jack Callaghan and Kevin Gillespie for helpful advice throughout this project.

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Authors and Affiliations

  1. Motion Analysis Laboratory, Shriners Hospitals for Children, 1645 West 8th Street, Erie, PA, 16505, USA

    Matthew R. Walker

  2. Department of Human Health and Nutritional Sciences, ANNU 334, University of Guelph, Guelph, ON, Canada, N1G 2W1

    James P. Dickey

Authors
  1. Matthew R. Walker
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  2. James P. Dickey
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Correspondence to James P. Dickey.

Additional information

All research accomplished at: Department of Human Health and Nutritional Sciences, University of Guelph, Guelph ON, Canada.

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Walker, M.R., Dickey, J.P. New methodology for multi-dimensional spinal joint testing with a parallel robot. Med Bio Eng Comput 45, 297–304 (2007). https://doi.org/10.1007/s11517-006-0158-6

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  • DOI: https://doi.org/10.1007/s11517-006-0158-6

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