Solution to the Inverse Problem of the Angular Manipulator Kinematics with Six Degrees of Freedom

New analytical solutions for the inverse kinematics problem of a 6R manipulator are proposed. Based on the assumption that the rotation axes of the last three links intersect at a common point, the problem is divided into orientation and transition problems. The position of the common point and the rotation angles of the first three links are determined using the equations of motion of the output link. A matrix equation for the rotation angles of the last three links is formulated. Solutions to the inverse kinematics problem are obtained for three models. In the first two, the rotation axis of the fourth link may not intersect the vertical rotation axis of the first. In the third model, the rotation axis of the fourth link intersects neither the vertical rotation axis of the first link nor the intersection point of the axes of the last two links. For all models, an analytical solution in closed form is obtained from the geometry of the mechanism. The solution for the third requires a preliminary search for the root of the transcendental equation for the rotation angle of the fourth link. Illustrative examples of calculations for a specific manipulator are given.