Motion Interpolation and Quaternions

 
• Angeles, J., Fundamentals of Robotic Mechanical Systems, 1996, Springer Verlag.
• Angeles, J., Rational Kinematics, 1980, Springer Verlag.
• Beggs, J. S., Kinematics, 1983, Hemishpere Publishing Company.
• Bottema, O., and Roth, B., Theoretical Kinematics, 1979, North Holland Publishing Company.
• Dijksman, E. A., Motion Geometry of Mechanisms, 1976, Cambridge University Press.
• Erdman, A. G. and Sandor, G. N., Mechanism Design: Analysis and Synthesis: Vol. 1, 1996, Prentice Hall.
• Flanders, H, Differential Forms with Applications to the Physical Sciences, 1963, Academic Press.
• Karger, A., and Novak, J., Space Kinematics and Lie Groups, 1978, Gordon and Breach Science Publishers.
• McCarthy, J. M., Introduction to Theoretical Kinematics, 1990, MIT Press.
• Nikravesh, P. E., Computer-Aided Analysis of Mechanical Systems, 1988, Prentice Hall.
• Norton, R. L., Design of Machinery: An Introduction to the Synthesis and Analysis of Mechanisms and Machines, 1st Edition, 1992, McGraw Hill.
• Sandor, G. N. and Erdman, A. G., Mechanism Design: Analysis and Synthesis: Vol. 2, 1994, Prentice Hall.
• Shigley, J. E. and Uicker, J. J., Theory of Machines and Mechanisms, 1995, McGraw Hill.
• Tyson, H. N., Kinematics, 1966, John Wiley.
• Wilson, C. E., and Sadler, J. P., Kinematics and Dynamics of Machinery, 2nd Edition, 1993, Harper Collins.

• Ahrikencheikh, C., Seireg, A. A., and Ravani, B., Optimal and Conforming Motion of a Point in a Constrained Plane, ASME Journal of Mechanical Design, Vol. 116, 1994, pp. 474-479.
• Barr, A. H., Currin, B., Gabriel, S., and Hughes, J. F., Smooth Interpolation of Orientation With Velocity Constraints, Computer Graphics, Vol. 26, No. 2, 1992, pp. 313-320.
• Ge, Q. J., and McCarthy, J. M., The Algebraic Classification of the Image Curves of Spherical Four Bar Motion, ASME Journal of Mechanical Design, Vol. 113, 1991, pp. 227-231.
• Ge, Q. J., and McCarthy, J. M., Functional Constraints as Algebraic Manifolds in a Clifford Algebra, IEEE Transactions on Robotics and Automation, Vol. 7, No. 5, 1991, pp. 670-677.
• Ge, Q. J., and Ravani, B., On Representation of Line-Segments for Computer-Aided Geometric Design, Proceedings of the 1994 ASME Automation Conference, DE-Vol. 69-1, 1994, pp. 191-198.
• Ge, Q. J., and Ravani, B., Geometric Construction of Bezier Motions, ASME Journal of Mechanical Design, Vol. 116, 1994, pp. 749-755.
• Ge, Q. J., and Ravani, B., Computer Aided Geometric Design of Motion Interpolants, ASME Journal of Mechanical Design, Vol. 116, 1994, pp. 756-762.
• Ge, Q. J., and Ravani, B., Computation of Spatial Displacements from Redundant Geometric Features, ASME Journal of Mechanical Design, Vol. 116, 1994, pp. 1073-1080.
• Ge, Q. J., and Kang, D., Motion Interpolation with G2 Composite Bezier Motions, Proceedings of the 1994 ASME Design Automation Conference, DE-Vol. 69-1, 1994, pp. 183-190.
• Ge, Q. J., and Kang, K., Motion Interpolation with G2 Composite Bezier Motions, ASME Journal of Mechanical Design, Vol. 117, 1995, pp. 520-525.
• Ge, Q. J., and Ravani, B., Computational Geometry and Motion Approximation, Computational Kinematics, J. Angeles eds., 1993, pp. 229-238.
• Gibson, C. G., and Hunt, K. H., Geometry of Screw Systems I, Mechanism and Machine Theory, Vol. 25, No. 1, 1990, pp. 1-10.
• Gibson, C. G., and Hunt, K. H., Geometry of Screw Systems II, Mechanism and Machine Theory, Vol. 25, No. 1, 1990, pp. 11-27.
• Hart, J. C., Francis, G. K., and Kauffman, L. H., Visualizing Quaternion Rotation, ACM Transactions on Graphics, Vol. 13, No. 3, 1994, pp. 256-276.
• Juttler, B., Visualization of Moving Objects Using Dual Quaternion Curves, Computers and Graphics, Vol. 18, No. 3, 1994, pp. 315-326.
• Juttler, B., and Wagner, M. G., Computer-Aided Design With Spatial Rational B-Spline Motions, ASME Journal of Mechanical Design, Vol. 118, 1996, pp. 193-201.
• Kim, D. S., Papalambros, P. Y., and Woo, T. C., Tangent, Normal, and Visibility Cones on Bezier Surfaces, Computer Aided Geometric Design, Vol. 12, 1995, pp. 305-320.
• Kim, M-J., Kim, M-S., and Shin, S. Y., A General Construction Scheme for Unit Quaternion Curves with Simple High Order Derivatives, Proceedings of the ACM SIGGRAPH Conference, 1995, pp. 369-376.
• Kim, M-S., and Nam, K-W., Interpolating Solid Orientations with Circular Blending Quaternion Curves, Computer Aided Design, Vol. 27, No. 5, 1995, pp. 385-398.
• Louduha, T. A., and Ravani, B., Motion Interpolation Using Dynamics, Proceedings of the 1994 ASME Design Automation Conference, DE-Vol. 69-1, 1994, pp. 175-181.
• McCarthy, J. M., The Differential Geometry of Curves in an Image Space of Spherical Kinematics, Mechanisms and Machine Theory, Vol. 22, No. 3, 1987, pp. 205-211.
• McCarthy, J. M., and Ravani, B., Differential Kinematics of Spherical and Spatial Motions Using Kinematic Mapping, ASME Journal of Applied Mechanics, Vol. 53, 1986, pp. 15-22.
• Park, F. C., and Ravani, B., Smooth Invariant Interpolation of Rotations, ACM Transactions on Graphics, Vol. 16, No. 3, 1997, pp. 277-295.
• Park, F. C., and Ravani, B., Bezier Curves on Riemannian Manifolds and Lie Groups with Kinematic Applications, ASME Journal of Mechanical Design, Vol. 117, 1995, pp. 36-40.
• Pletinckx, D., Quaternion Calculus as a Basic Tool in Computer Graphics, The Visual Computer, Vol. 5, 1989, pp. 2-13.
• Ramamoorthi, R., and Barr, A. H., Fast Construction of Accurate Quaternion Splines, Proceedings of the ACM SIGGRAPH Conference on Computer Graphics, 1997, pp. 287-292.
• Ravani, B., and Roth, B., Mappings of Spatial Kinematics, ASME Journal of Mechanisms, Transmissions, and Automation in Design, Vol. 106, 1984, pp. 341-347.
• Ravani, B., and Wang, J. W., Computer Aided Geometric Design of Line Constructs, ASME Journal of Mechanical Design, Vol. 113, 1991, pp. 363-371.
• Ravani, B., and Ge, Q. J., Computation of Spatial Displacements from Geometric Features, ASME Journal of Mechanical Design, Vol. 115, 1993, pp. 95-102.
• Reeves, W. T., Inbetweening for Computer Animation Utilizing Moving Point Constraints, Computer Graphics, Vol. 15, No. 3, 1981, pp. 263-269.
• Shoemake, K., Animating Rotations With Quaternion Curves, Computer Graphics, Vol. 19, No. 3, 1985, pp. 245-254.
• Sprott, K., and Ravani, B., Ruled Surfaces, Lie Groups, and Mesh Generation, Proceedings of the 1997 ASME Design Engineering Technical Conference.
• Sprott, K., and Ravani, B., A Dynamic Formulation for Planar Motions Using Geometric Kinematics and CAGD, Computational Kinematics, J. P. Marlet and B. Ravani eds., 1995, pp. 301-310.
• Srinivasan, L. N., and Ge, Q. J., Parametric Continuity and Smooth Motion Interpolation, Proceedings of the 1992 ASME Design Engineering Technical Conference, DE-Vol. 82, 1995, pp. 665-672.
• Srinivasan, L. N., and Ge, Q. J., Parametric Continuous and Smooth Motion Interpolation, ASME Journal of Mechanical Design, Vol. 118, 1996, pp. 494-498.
• Srinivasan, L. N., and Ge, Q. J., Fine Tuning of Rational B-Spline Motions, Proceedings of the 1997 ASME Design Engineering Technical Conference.
• Zefran, M., and Kumar, V., Planning of Smooth Motions on SE(3), Proceedings of the 1996 IEEE International Conference on Robotics and Automation, 1996, pp. 121-126.
• Zefran, M., Kumar, V., and Croke, C., On the Generation of Smooth Three-Dimensional Rigid Body Motions, Submitted to the IEEE Transactions on Robotics and Automation.
• Zefran, M., Kumar, V., and Croke, C., Metrics and Connections for Rigid Body Kinematics, Submitted to the International Journal of Robotics Research.