Lie groups and Lie algebras in robotic motions

Kinematics is a branch of mechanics that does not contain the concepts of force and mass. That is, Kinematics just examines the time dependent change in the location of a point or a point system ( the body ).Kinematic modeling which science of robotics is one of the most important analytical tools are used in many fields of science of robotics. In particular: Mechanisms, modeling of sensors and actuators, concurrent robot control applications, robot simulation and programming a synchronous transactions. Robot kinematic modeling of robots is one of the most important stages of the work of robotics. Cartesian plane, using conversion-operators such as matrix or vectors, was called point conversion to this method is removed from the kinematic model. Further, If linear transformation vectors and the operators are used, then this method is called a linear transformation method. Using transformation cartesian plane of vectors, Maxwell described the 4x4 homogeneous transformation matrix. Denavit-Hartenberg, using the homogeneous transformation matrix, orientation and position of a coordinate system defined by the coordinate system to another. According to a coordinate system to another, transformation matrix can be expressed the movement of the screw. In this method expressed as a linear transformation takes both a displacement and rotation on the same axis.In this study, we made mind earlier these studies, differently, Lie groups and Lie algebras in robotic motions and will explore with the limited movement of the screw.Keywords: Lie Group, Lie Algebra, Robots, Motion, Rotational