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Selig, JM (2007)
Languages: English
Types: Unknown
Subjects:
The classical subject of planar kinematics is reviewed in the setting of Lie algebra and differential geometry. In particular, the classical centrode curves of a rigid motion are related to the derivatives in the Lie algebra. The classical subject of planar kinematics is reviewed in the setting of Lie algebra and differential geometry. In particular, the classical centrode curves of a rigid motion are related to the derivatives in the Lie algebra. Several examples of finding centrode curves in different situations are given. The case where a rigid motion is determined by one curve rolling on another is studied in some detail.
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    • [1] O. Bottema and B. Roth. Theoretical Kinematics. Dover Publications, New York, 1990.
    • [2] C.G. Gibson. Elementary geometry of differentiable curves. Cambridge University Press, 2001.
    • [3] F. Hausdorff. Die Symbolische exponential formel in den grupen theorie. Berichte de Sa¨chichen Akademie de Wissenschaften (Math Phys Klasse) 58:19–48, 1906.
    • [4] K.H. Hunt. Kinematic Geometry of Mechanisms. Clarendon Press, Oxford, 1990.
    • [5] J.M. Selig. Geometric Fundamentals of Robotics. Springer Verlag, New York, 2005.
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