Abstract
This paper presents a method for kinematic registration in three dimensions using a classical technique from two-dimensional kinematics, namely the Reuleaux method. In three dimensions the kinematic registration problem involves reconstruction of a spatial displacement from data on a minimum of three homologous points at two finitely separated positions of a rigid body. When more than the minimum number of homologous points are specified or when errors in specification of these points are considered, the problem becomes an over determined approximation problem. A computational geometric method is presented, resulting in a linear solution of the over determined system. The results have applications in robotics, manufacturing, and biomedical imaging. The paper considers the kinematic registration when minimal, over-determined, infinitesimal, and perturbed sets of homologous point data are given.
Issue Section:
Research Papers
1.
Reuleaux
, F.
, 1876, Theoretische Kinematik: Grundzüge einer Theorie des Maschinenwesens
; the English translation is: Kinematics of Machinery. Outlines of a Theory of Machines
, trans., and ed. by Alex
, B. W.
Kennedy
, C. E.
, MacMillan
, London
.2.
Bottema
, O.
, and Roth
, B.
, 1990, Theoretical Kinematics
, Dover
, New York
(Corr. reprint of the 1979 edition, North-Holland, Amsterdam).3.
Frankel
, V. H.
, Burstein
, V. H.
, and Brooks
, D. B.
, 1971, “Biomechanics of Internal Derangement of the Knee: Pathomechanics as Determined by Analysis of the Instant Centers of Motion
,” J. Bone Jt. Surg., Am. Vol.
0021-9355, 53A
, pp. 945
–962
.4.
Grant
, P. G.
, 1973, “Biomechanical Significance of the Instantaneous Center of Rotation: The Human Temporomandibular Joint
,” J. Biomech.
0021-9290, 6
, pp. 109
–113
.5.
Haher
, T. R.
, O’Brien
, M.
, Felmly
, W. T.
, Welin
, D.
, Perrier
, G.
, Choueka
, J.
, Devin
, V.
, Vassiliou
, A.
, and Chow
, G.
, 1992, “Instantaneous Axis of Rotation as a Function of the Three Columns of the Spine
,” Spine
0362-2436, 17
, pp. 149
–154
.6.
Tamea
, C.
, and Henning
, C.
, 1981, “Pathomechanics of the Pivot Shift Mechanism
,” An. R. Acad. Nac. Med. (Madr)
0034-0634, 9
, pp. 31
–37
.7.
Nederbragt
, W. W.
, and Ravani
, B.
, 2005, “Enumeration of Contact Geometries for Part Registration in Design of Tactile Sensing Fixtures
,” Trans. ASME, J. Mech. Des.
(in press).8.
Pottmann
, H.
, Leopoldseder
, S.
, and Hofer
, M.
, 2002, “Simultaneous Registration of Multiple Views of a 3D Object
,” Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, XXXIV
, Part 3A, Commission III, pp. 265
–270
.9.
Pottmann
, H.
, Leopoldseder
, S.
, and Hofer
, M.
, 2004, “Registration Without ICP
.” Comput. Vis. Image Underst.
1077-3142, 95
(1
), pp. 54
–71
.10.
11.
Beggs
, J. S.
, 1983, Kinematics
, Hemisphere
, Washington D.C.
.12.
Suh
, C. H.
, and Radcliffe
, C. W.
, 1978, Kinematics and Mechanisms Design
, Wiley
, New York
.13.
Chen
, J.-Y.
, Birk
, J. R.
, and Kelley
, R. B.
, 1980, “Estimating Workpiece Pose Using the Feature Points Method
,” IEEE Trans. Autom. Control
0018-9286, AC-25
(6
).14.
Laub
, A. J.
, and Shiflett
, G. R.
, 1982, “A Linear Algebra Approach to the Analysis of Rigid Body Displacement from Initial and Final Position Data
,” Trans. ASME, J. Appl. Mech.
0021-8936, 49
, pp. 213
–216
.15.
Laub
, A. J.
, and Shiflett
, G. R.
, 1983, “A Linear Algebra Approach to the Analysis of Rigid Body Velocity from Position and Velocity Data
,” , 105
, pp. 92
–95
.16.
Rossignac
, J. R.
, and Kim
, J. J.
, 2001, “Computing and Visualizing Pose-Interpolating 3D Motions
,” Comput.-Aided Des.
0010-4485, 33
(4
), pp. 279
–291
.17.
Hiller
, M.
, and Woernle
, C. A.
, 1984, “Unified Representation of Spatial Displacements
,” Mech. Mach. Theory
0094-114X, 19
(6
), pp. 477
–486
.18.
Angeles
, J.
, 1986, “Automatic Computation of the Screw Parameters of Rigid-Body Motions. Part I: Finitely-Separated Positions
,” Trans. ASME, J. Dyn. Syst. Meas.
0022-0434, 108
, pp. 32
–38
.19.
Angeles
, J.
, 1986, “Automatic Computation of the Screw Parameters of Rigid-Body Motions. Part II: Infinitesimally-Separated Positions
,” Trans. ASME, J. Dyn. Syst. Meas.
0022-0434, 108
, pp. 39
–43
.20.
Ravani
, B.
, and Ge
, Q. J.
, 1993, “Computation of Spatial Displacements from Geometric Features
,” ASME J. Mech. Des.
1050-0472, 115
, pp. 95
–102
.21.
Horn
, B. K. P.
, 1987, “Closed-form Solution of Absolute Orientation using Unit Quaternions
,” J. Opt. Soc. Am.
0030-3941, 4
(4
), pp. 629
–642
.22.
Ge
, Q. J.
, and Ravani
, B.
, 1994, “Computation of Spatial Dispacements from Redundant Geometric Features
, ASME J. Mech. Des.
1050-0472, 116
, pp. 1073
–1080
.23.
Shiflett
, G. R.
, and Laub
, A. J.
, 1995, “The Analysis of Rigid Body Motion from Measured Data
,” Trans. ASME, J. Dyn. Syst. Meas.
0022-0434, 117
, pp. 578
–584
.24.
Plücker
, J.
, 1868, Neue Geometrie des Raumes, gegründet auf die Betrachtung der geraden Linie als Raumelement
, Teubner
, Leipzig
, Germany, Vol. 1
.25.
Farin
, G.
, and Hansford
, D.
, 1998, The Geometry Toolbox for Graphics and Modeling
, A. K. Peters
, Natick, Mass.
.26.
Boehm
, W.
, and Prautzsch
, H.
, 1993, Numerical Methods
, Viewweg, Wiesbaden, and A. K. Peters
, Wellesley
.27.
Eberharter
, J. K.
, and Ravani
, B.
, 2004, “Kinematic Registration using Line Geometry
,” International Design Engineering Technical Conf. & Comp. and Information in Engineering Conference, ASME-DETC
, Sept. 28–Oct. 2, Salt Lake City
, Utah.28.
Pottmann
, H.
, Peternell
, M.
, and Ravani
, B.
, 1999, “An Introduction to Line Geometry With Applications
,” Comput.-Aided Des.
0010-4485 31
, pp. 3
–16
.29.
Hlavatý
, V.
, 1953, Differential Line Geometry
, Nordhoff
, Groningen, Holland
.30.
Pottmann
, H.
, and Wallner
, J.
, 2001, Computational Line Geometry
, Springer
, Berlin
.31.
Weiss
, E. A.
, 1935, Einführung in die Liniengeometrie und Kinematik
, Teubners mathematische Leitfäden, Band, 41
, Leipzig, und Druck von B. G. Teubner.Copyright © 2006
by American Society of Mechanical Engineers
You do not currently have access to this content.
