Structures of Kinematic Models of a Walking Machine Using Motor Algebra

Abstract

The forward and inverse kinematics of a walking machine are modeled and analysed in a unified manner using the motor algebra. First, the velocity motor of a link is defined to specify the motion of the link. Then, by changing the reference point and the frame of the velocity motor of each link to other ones consecutively along the link-pair graph, the independent closed link conditions are derived, which are linear with respect to the joint angle velocity, the velocity of the trunk, and the angular velocity of the trunk. The inverse kinematics can be solvable if the image of an induced linear map of the velocity and angular velocity of the trunk belongs to the image of an induced linear map of the joint angle velocity. By a numerical analysis of the induced linear spaces of the inverse kinematics which models a walking machine with a planar pantograph leg whose toe contacts the ground, independent solutions of the velocity and angular velocity of the trunk are obtained, each of which has the corresponding joint angle velocity.