Inverse kinematics of a reclaimer: Closed-form solution by exploiting geometric constraints

The inverse kinematics of a reclaimer that excavates and transports raw materials in a raw yard is investigated. Because of the geometric feature of the equipment, in which scooping buckets are attached around a rotating disk, kinematic redundancy occurs in determining the joint variables. Link coordinates are introduced following the Denavit-Hartenberg representation For a given excavation point the forward kinematics yields 3 equations in 4 variables. It is shown that the rotating disk at the end of the boom provides an extra passive degree of freedom. Two approaches are investigated in obtaining an inverse kinematics solution. The first method pre-assigns the height of the excavation point, which can be determined through path planning. A closed-form solution is obtained for the first approach. The second method exploits the orthogonality between the normal vector at an excavation point and the z-axis of the end-effector coordinate system. The geometry near the reclaiming point has been approximated as a plane, and the plane equation has been obtained by a least-squares method from 8 adjacent points near the point. A closed-form solution is not found for the second approach; however, a linear approximate solution is provided.