Dynamics of Mechanical Systems with Mecanum Wheels

The kinematics and dynamics of a mechanical system with mecanum wheels is studied. A mecanum wheel is a wheel with rollers attached to its circumference. Each roller rotates about an axis that forms an angle with the plane of the disk (for the omni-wheels, the axes of the rollers lie in the plane of the wheel and in an ideal case are tangent to the outer circumference of the wheel). Such a design provides additional kinematic advantages for the mecanum wheels in comparison with the conventional wheels. Within the framework of non-holonomic mechanics, the equations of motion are derived for the case of an arbitrary angle at which the rollers are attached (usually, this angle is assumed to be equal to 45°). In robotics, a simplified approach, in which the equations of non-holonomic kinematic constraints are solved approximately by means of a pseudo-inverse matrix, is frequently applied. Such an approximate approach leads to “holonomization” of the system and allows Lagrange’s equations of the second kind to be used. In the present paper, the equations of motion obtained on the basis of the principles of non-holonomic mechanics are compared with the approximate equations. It is shown that for translational motions and for the rotation of the system about its center of mass, both these approaches lead to the same result.