Calculation of the robot manipulator dynamic equations

New method for efficient calculation of the robot manipulator kinematics and dynamics is presented. It is based on the use of second order LaGrange equations and allow to describe dynamics of manipulators with rotation and translation joints. Equations have matrix form, allow solving both direct and inverse dynamics problems, providing high calculation efficiency. Structure of the equations allows applying symbolic calculations to derive equations in symbolic form. This increases calculation efficiency up to 4-5 times for 2 and 3 links manipulators. Models of the torque in manipulator joints are presented. It takes into account joint's elasticity and various non-linearities such as friction, backlashes, limits on current and voltage and maximum torque value.