This paper presents an accurate and robust approach for determining the kinematic parameters of biomechanical systems. A computationally efficient algorithm is given for estimating the translation vector and rotation matrix of a moving body from measurements of the position of at least four spatially distributed points on the body. This algorithm provides an estimation of the spatial location and orientation of the body which is less sensitive to measurement error than other methods. It is indicated how the kinematic parameters can be used to determine the linear translation and angular rotation of the moving body in terms of an anatomically relevant coordinate system. The design, fabrication and calibration of an inexpensive, serial-link, three-dimensional mechanical digitizer for use in data acquisition is described. This device is kinematically optimized and is easy to use for accurate data collection. An implementation of this approach to quantifying certain aspects of the kinematics of the human wrist is discussed.
Get full access to this article
View all access options for this article.
References
1.
ReddyN. P.AskewM. J.BaniewiezF. M.MelbyA.IIIFullerK. A.SteurerP. A.HerrJ. E.ShefferD. E.A technique for quantitative assessment of three-dimensional motion with applications to human joints. Proc. Instn Mech. Engrs, Part H, 1989, 203, 207–213.
2.
KinzelG. L.GutkowskiL. J.Joint models, degrees of freedom, and anatomical motion measurement. J. Biomech. Engng, February 1983, 105, 55–62.
3.
GallowayR. L.EdwardsC. A.HadenG. L.MaciunasR. J.A three-dimensional locating pointer for stereotactic neurosurgery. Proceedings of IEEE Conference on Engineering in medicine and biology, Seattle, Wash., October1989 (IEEE).
4.
ShiaviR.LimbirdT.FrazerM.StiversK.StraussA.AbramovitzF.Helical motion analysis of the knee—I. Methodology for studying kinematics during locomotion. J. Biomechanics, 1987, 20(5), 459–469.
5.
AnK.N.JacobsenM. C.BerglundL. J.ChaoE. Y. S.Application of a magnetic tracking device to kinesiologic studies. J. Biomechanics, 1988, 21(7), 613–620.
6.
LangranaN. A.Spatial kinematic analysis of the upper extremity using a biplanar videotaping method. J. Biomech. Engng, February 1981, 103, 11–17.
7.
MillerN. R.ShapiroR.McLaughlinT. M.A technique for obtaining spatial kinematic parameters of segments of bio-mechanical systems from cinematographic data. J. Biomechanics, 1980, 13, 535–547.
8.
GroodE. S.SuntayW. J.A joint coordinate system for the clinical description of three-dimensional motions: Application to the knee. J. Biomech. Engng, May 1983, 105, 136–144.
9.
YoumY.YoonY.Analytical development in investigation of wrist kinematics. J. Biomechanics, 1979, 12, 613–621.
10.
WoltringH. J.HuiskesR.De LangeA.VeldpausF. E.Finite centroid and helical axis estimation from noisy landmark measurements in the study of human joint kinematics. J. Biomechanics, 1985, 18, 379–389.
11.
LlewellynJ. A.BelsoleR. S.DaleM. M.HilbelinkR. D.StenzlerS. A.Geometry of the wrist. Proceedings of IEEE Conference on Engineering in medicine and biology, Seattle, Wash., October1989 (IEEE).
12.
AngelesJ.Automatic computation of the screw parameters of rigid-body motions. Parts I and II. J. Dynamic Systems, Measmt, and Control, March 1986, 108, 32–43.
13.
VeldpausF. E.WoltringH. J.DortmansL. J. M. G.A least-squares algorithm for the equiform transformation from spatial marker coordinates. J. Biomechanics, 1988, 21, 45–54.
14.
SpoorC. W.VeldpausF. E.Rigid body motion calculated from spatial coordinates of markers. J. Biomechanics, 1980, 13, 391–393.
15.
LawsonC.HansonR.Solving least squares problems, 1974 (Prentice-Hall, Englewood Cliffs, N.J.).
16.
StrangG.Linear algebra and its applications, 3rd edition, 1988 (Harcourt Brace Jovanovich Publishers).
17.
HighamN. J.Computing the polar decomposition: With applications. SIAM J. Sci. Stat. Computing, October 1986, 7(4), 1160–1174.
CraigJ.Introduction to robotics: mechanics and control, 1987 (Addison-Wesley, Reading, Mass.).
20.
ColbaughR.GlassK.Cartesian control of redundant robots. J. Robotic Systems, 1989, 6(4), 427–459.
21.
HollerbachJ. M.Optimum kinematic design for a seven degree of freedom manipulator. Proceedings of Second International Symposium on Robotics research, Cambridge, Mass., 1985, pp. 216–222.
22.
WamplerC. W.IIInverse kinematics of a 7 DOF manipulator. NATO Advanced Research Workshop on Robots with redundancy: design sensing and control, Salo, Lago di Garda, Italy, 27 June-1 July 1988 (NATO).
23.
ColbaughR.SerajiH.GlassK.Obstacle avoidance for redundant robots using configuration control. J. Robotic Systems, 1989, 6(6), 721–744.
24.
KleinC. A.BlahoB. E.Dexterity measures for the design and control of kinematically redundant manipulators. Int. J. Robotics Res., 1987, 6(2), 72–83.
25.
YoshikawaT.Manipulability and redundancy control of robotic mechanisms. Proceedings of IEEE International Conference on Robotics and automation, St Louis, Mo., March 1985 pp. 1016–1021 (IEEE).
26.
HayatiS.MirmiraniM.Improving the absolute positioning accuracy of robot manipulators. J. Robotic Systems, 1985, 397–413.
27.
HayatiS.TsoK.RostotG.Robot geometry calibration. Proceedings of IEEE International Conference on Robotics and automation, Philadelphia, Pa., April 1988 pp. 947–951 (IEEE).
28.
SmithD. K.CooneyW. P.IIIAnK. N.LinscheidR. L.ChaoE. Y. S.The effects of simulated unstable scaphoid fractures on carpal motion. J. Hand Surg., March 1989, 14A(2), Part 1, 283–290.
29.
RowenB.An experimental summary of wrist kinematics, Texas Tech University Biomechanics memorandum 91–02, 1991.
30.
ColbaughR.GlassK.Hierarchical control of human joint motion simulators. Computers and Electrical Engng: An Int. J., 1993, 19(1).
