A Transmission Quality Index for a Class of Four-Limb Parallel Schönflies Motion Generators

Abstract

This paper presents a uniform method of evaluating both transmission quality and singularity applicable for a class of parallel Schönflies-motion generators (SMGs) with four RRΠRR limbs. It turns out that the determinant of the forward Jacobian matrices for this class of parallel robots can be expressed as the scalar product of two vectors, the first vector being the cross product of the four unit vectors along the parallelograms, and the second one being related to the rotation of the mobile platform (MP). The pressure angles, derived from the determinants of forward and inverse Jacobians, respectively, are used for the evaluation of the transmission quality and the detection of robot singularities. Four robots are compared based on the proposed indices as illustrative examples.

A four-limb parallel Schönflies motion generator with full-circle end-effector rotation

“…In accordance with the singularity analysis of this four-limb parallel SMG [33,34], the constraint singularity usually occurs when at least two of the parallelograms are parallel or the rotational sub-platform lies in the plane determined by the two parallelograms in the first and third limbs [9]:…”

“…From the perspective of workspace quality, the proposed robot can have a relatively large fullrotation workspace free of singularity versus the robot footprint, rather than some existing four-limb SMGs as revealed in our previous work [34]. Moreover, in comparison with the four-limb SMG end-effectors with different shape and size corresponding to different orientations, e.g., belt-pulley mechanism [4], the rack-pinion mechanism [3], gears and screw mechanism [5], an advantage is that the articulated transmitting mechanism can be sealed in the gearbox, which eases the cleaning procedure when the robot is deployed in the sector of food industry.…”

“…When the determinant |A| of the forward Jacobian matrix is equal to zero, the actuation singularity occurs in the case of the general linear complex. The wrench exerting on the end-effector is generated by one of the transmission wrenches that is proportional to those that are generated by the other transmission wrenches, thus, the robot loses 1-DOF motion in this singular configuration [34].…”

“…Type-1 singularity loci The type-1 singularity loci, which can be readily identified, are located on the reachable workspace boundaries [34]. Figure 4(a) displays all the possible type-1 singularity loci of limb 1 with constant end-effector orientation φ = 0, which are subject to the motion range of the actuated joints.…”

Evaluation of the Kinematic Performance of a 3-RRS Parallel Mechanism

“…In addition, some scholars found that the determinant of the Jacobian matrices for a class of parallel robots can be expressed as the scalar product of two vectors, and then the pressure angles, derived from the determinants of the Jacobians, can be used for the evaluation of the transmission quality, the detection of robot singularities, or the kinematic constraints of optimal design. [17][18][19] Since the reciprocal product of a unit wrench and a unit twist is irrelevant to the coordinate frame, the virtual coefficient was proposed. 20 Based on such a concept, a variety of kinematic performance evaluation indices, which are dimensionless and invariant with respect to the coordinate frame, are constructed.…”