A Dual Method to Study Motion of A Robot End-Effector
W. Blaschke, Vorlesungen Über Differentialgeometrie, Bd. 1, Dover Publications, New York (1945).
O. Bottema and B. Roth, Theoretical Kinematics, North-Holland Publ. Co., Amsterdam, p. 556 (1979).
M. Brady, J.M. Hollerbach, T.L. Johnson, T. Lozano-Perez and M.T. Mason, Robot Motion: Planning and Control, The MIT Press, Cambridge, Massachusetts, p. 585 (1982).
M.P. Do Carmo, Differential Geometry of Curves and Surfaces, Vol. 2, Prentice-hall, Englewood Cliffs (1976).
C. Ekici, Y. Ünlütürk, M. Dede and B.S. Ryuh, On motion of robot end-effector using the curvature theory of timelike ruled surfaces with timelike ruling, Mathematical Problems in Engineering 2008 (2008), Article ID 362783.
H.H. Hacısalihoglu, On the pitch of a closed ruled surface, Mechanism and Machine Theory 7 (1972), 291 – 305.
H.H. Hacısalihoglu, Hareket Geometrisi ve Kuaterniyonlar Teorisi, Gazi University Faculty of Sciences and Arts (1983).
A. Karger and J. Novak, Space Kinematics and Lie Groups, STNL Publishers of Technical Lit., Prague, Czechoslovakia (1978).
A.P. Kotelnikov, Screw Calculus and Some Applications to Geometry and Mechanics, Annals of Imperial University of Kazan (1895).
F.L. Litvin and X.C. Gao, Analytical representation of trajectory of manipulators, trends and developments in mechanisms, machines, and robotics, The ASME Design Technology Conferences, the 20th Biennial Mechanisms Conference, Vol. 15-3, pp. 481 – 485, Kissimmee, Florida, USA, September 25-28 (1988).
R.P. Paul, Manipulator cartesian path control, IEEE Trans. Systems, Man., Cybernetics SMC-9 (11) (1979), 702 – 711.
B.S. Ryuh, Robot Trajectory Planning Using the Curvature Theory of Ruled Surfaces, Doctoral dissertation, Purdue University, West Lafayette, Ind., USA (1989).
B.S. Ryuh and G.R. Pennock, Accurate motion of a robot end-effector using the curvature theory of ruled surfaces, Journal of Mechanisms, Transmissions, and Automation in Design 110 (4) (1988), 383 – 388.
B.S. Ryuh and G.R. Pennock, Trajectory planning using the Ferguson curve model and curvature theory of a ruled surface, Journal of Mechanical Design 112 (1990), 377 – 383.
J.A. Schaaf, Curvature Theory of Line Trajectories in Spatial Kinematics, Doctoral dissertation, University of California, Davis, 111 p. (1988).
E. Study, Geometrie der Dynamen, Leipzig (1903).
G.R. Veldkamp, On the use of dual numbers, vectors and matrices in instantaneous spatial kinematics, Mechanism and Machine Theory II (1976), 141 – 156.
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