Forward and Inverse Kinematics
摘要
As mentioned in Sect. 1.3 , the joints of SKChs can be revolute or prismatic and the corresponding joint variables were established to be \(\theta \) and b, respectively. Throughout this chapter and the following ones, the terms arrangement, architecture, configuration, and pose are applied, whose definition is provided in Sect. 2.4. When a value is specified for each of the joint variables of a SKCh, its configuration is established, and it is possible to determine the pose of the end-effector. The process of obtaining the latter is known as Forward Kinematics, whereas Inverse Kinematics is the known process that determines the values of the joint variables that take the SKCh to a specified end-effector pose. It is worth mentioning that the inverse kinematics solution can lead to more than one configuration of the SKCh. Furthermore, proximal and distal notations, as studied in Sect. 1.3 , are embraced, and from the point of view of the forward kinematics problem, it is proven that their solution differs, in most cases, by one screw motion. It is also demonstrated that they reach the same solution in cases in which a spherical wrist is located at the end of the kinematical chain.