“…Researchers have faced difficulties in analyzing the motion equation in task-space since the exact kinematics model is not available in practice or surplus of sensors is required to monitor the motion of an end-effector. To deal this problem, let us consider the transformation functions as follows 49) and (50) to equation (47) and using(28)(29)(30), it can be obtained ( ,̇,̇,̈) = ( ,̇,̇,̈)(51)Using (51) and also transforming the error dynamics (33) into joint space, i.e. = (̇−̇), equation (48) can be modified as ̇= ( (̇−̇)) ( − − ( ,̇,̇,…”