Introduction to Kinematics of Manipulators using Maple Roman Hasek hasek@pf.jcu.cz Pedagogical faculty, University of South Bohemia Ceske Budejovice, Czech Republic Computer algebra systems (CAS) enable teachers to bring various real-world problems into classrooms. These programmes provide students and teachers with means to develop symbolic representation of selected real-world problems, model them graphically and solve them symbolically or numerically. Such process, closed with solution and a functional model, is in our opinion very beneficial to develop true understanding of all utilized mathematical terms. The paper aims to present several examples that are closely connected to kinematics of serial robot-manipulators---forward and inverse kinematic problems and a velocity problem. We will see that kinematics of simple mechanisms (at the beginning we can restrict ourselves to planar mechanisms) represent real and attractive problems whose solving require mostly basic knowledge of linear algebra, geometry, differential geometry and of methods of solving systems of nonlinear algebraic equations. Suitable utilization of CAS relieves students of intricate computation and formulas manipulation and gives them opportunity to concentrate on the basic facts. Moreover the graphical and programming tools of CAS enable us to build simple both planar and spatial movable models of respective manipulators. Some of the problems are introduced in courses of geometry and linear algebra within the mathematics teacher training programmes at the Pedagogical faculty of the University of South Bohemia. The forward kinematic problem serves as an illustration of the connection between linear algebra and geometry, particularly between matrices and geometric transformations. Examples corresponding to the inverse kinematic problem are used as means of introduction to the solving of systems of nonlinear equations. More complex problems are assigned as student projects in the subject ``Solving problems using Maple'' which is one of those preparing students of teaching to use CAS programmes in education. The Pedagogical faculty of the University of South Bohemia educates teachers of mathematics for both elementary and secondary schools. Students of mathematics teaching are familiarized with the CAS software Derive, Maple and Mathematica during their study. Each of these programs plays its unique role in the teacher training. The Derive 6 software in its Czech localization is, in our opinion, the most convenient to adopt in the education of mathematics at elementary and secondary schools. In 2004 we started with systematic preparation, of both students of mathematics teaching and teachers of mathematics, in using this software. The Maple and Mathematica software is mainly used to support the teaching and study of mathematical academic courses.