Computations in robotics cover a rich spectrum of problems at the junction of mechanics, computer science, engineering and mathematics. In this talk the emphasis will be given to robot kinematics, its analysis, design and optimization with respect to different tasks. This will include a brief discussion on the direct and inverse kinematics problems of serial and parallel mechanisms, kinematic singularities, workspace determination, manipulability, as well as kinematic flexibility. Examples will present peculiarities in robot and human motion performing different tasks, such as the manipulation of heavy objects or the vertical jump, with the focus on kinematic redundancy. Redundant robots possess too many degrees of freedom; their number exceeds the number required by the task. Therefore, redundancy gives to the robot an immense source of freedom and enables it to solve different tasks in an infinite number of ways. The robot can simultaneously solve additional secondary tasks of lower priority. We will discuss various aspects in robot programming and design in comparison with humans.