Linear Dual Algebra Algorithms and their Application to Kinematics Ettore Pennestr` ı and Pier Paolo Valentini Universit`a di Roma Tor Vergata, via del Politecnico, 1 00133 Roma (Italy) pennestri@mec.uniroma2.it valentini@ing.uniroma2.it Summary. Mathematical and mechanical entities such as line vectors, screws and wrenches can be conveniently represented within the framework of dual algebra. Despite the applications received by this type of algebra, less developed appear the numerical linear algebra algorithms within the field of dual numbers. In this paper will be summarized different basic algorithms for handling vectors and matrices of dual numbers. It will be proposed an original application to finite and infinitesimal rigid body motion analysis. Key words: Clifford algebra, kinematics, screw motion 1 Introduction A dual number  a is an ordered pair of real numbers (a, a o ) associated with a real unit +1, and the dual unit, or operator ε, where ε 2 = ε 3 = ... = 0, 0ε = ε0 = 0, 1ε = ε1= ε . A dual number is usually denoted in the form  a = a + εa o . (1) A pure dual number has the dual unit only. The algebra of dual numbers has been originally conceived by W.K. Clifford (1873) [9], but its first applications to mechanics are due to A.P. Kotelnikov (1895) 1 and E. Study (1901) [26]. Dual vector algebra provides a convenient tool for handling mathematical entities such as screws and wrenches. In fact, helicoidal infinitesimal and finite rigid body displacements can be easily composed under the framework of dual vector algebra. Another distinctive feature of dual algebra is conciseness of notation. For these reasons it has been often used for the search of closed form solutions in the field of displacement analysis, kinematic synthesis and dynamic analysis of spatial mechanisms. Dual numbers and their algebra proved to be a powerful tool for the analysis of mechanical systems. Textbooks/monographies entirely dedicated to engineering applications of dual numbers have been authored to F.M Dimentberg [10], R. Beyer [5] and I.S. Fischer [13]. Books with chapters or sections on dual algebra and its applications have been authored by L. Brand [6], M.A. Yaglom [29], J.S. Beggs [4], J. Duffy [11], Gonz´ ales-Palacios and J. Angeles [15], J. McCarthy [20]. A more extensive list of references is given by E. Pennestr` ı and R. Stefanelli [22]. One of the purposes of this investigation is the development and implementation of algorithms for the solution of linear algebra problems using dual numbers. Although the algorithms discussed are mainly related to the solution of kinematic problems, we believe they are potentially useful also for dynamic analyses of mechanisms. The linear algebra algorithms herein presented can be splitted into the following categories: 1 The original paper of A.P. Kotelnikov, published in the Annals of Imperial University of Kazan (1895), is reputed to have been destroyed during the Russian revolution. [24]