Proc Lond Math Soc 4:381–395Ĭoolidge JL (2003) A history of geometrical methods. J Appl Mech 56:139–145Ĭlifford WK (1873) Preliminary sketch of bi-quaternions. Springer, Berlin/HeidelbergĬheng H, Gupta KG (1989) An historical note on finite rotations. In: Fuhrmann PA (ed) Mathematical theory of networks and systems. Cambridge University Press, Cambridgeīrockett RW (1984) Robotic manipulators and the product of exponentials formula. IEEE Trans Syst Man Cybern 28(2):135–145īall RS (1998) A treatise on the theory of screws. Celest Mech Dyn Astron 96(3–4):239–251Īspragathos NA, Dimitros JK (1998) A comparative study of three methods for robot kinematics. Turk J Math 32(4):373–391Īrribas M, Elipe A, Palacios M (2006) Quaternions and the rotation of a rigid body. In: Corrochano EB (ed) Geometric algebra with applications in science and engineering, Springer Verlag, Basel, pp 235–251Īkyar B (2008) Dual quaternions in spatial kinematics in an algebraic sense. The purpose of this chapter is to provide the basic mathematical tools and the main results for the kinematics of rigid body though many objects may have elastic deformation in practical engineering problems.Īhlers SG, McCarthy JM (2001) The Clifford algebra and the optimization of robot design. Then, an example of a SCARA robot is given to show the applications of the basic theoretical tools for rigid body motions. This chapter firstly presents the representation method of the position and orientation of rigid bodies using both the algebraic and the geometric methods. The kinematics of rigid body is the motion analysis without considering any external forces acting on a rigid body, which is actually the foundation of the dynamics of rigid bodies. ![]() For rigid body motions, the representations of rigid body rotation have a wide range of approaches including the representations from the directional cosine matrix to the exponential coordinates. ![]() Many physical objects are considered as rigid bodies for the convenience of theoretical analysis. Mechanism is made up of links and kinematic pair joints which move in the three-dimensional space.
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