A Novel 3-URU Architecture with Actuators on the Base: Kinematics and Singularity Analysis

Abstract

Translational parallel manipulators (TPMs) with DELTA-like architectures are the most known and affirmed ones, even though many other TPM architectures have been proposed and studied in the literature. In a recent patent application, this author has presented a TPM with three equal limbs of Universal-Revolute-Universal (URU) type, with only one actuated joint per limb, which has overall size and characteristics similar to DELTA robots. The presented translational 3-URU architecture is different from other 3-URUs, proposed in the literature, since it has the actuators on the frame (base) even though the actuated joints are not on the base, and it features a particular geometry. Choosing the geometry and the actuated joints highly affects 3-URU’s behavior. Moreover, putting the actuators on the base allows a substantial reduction of the mobile masses, thus promising good dynamic performances, and makes the remaining part of the limb a simple chain constituted by only passive R-pairs. The paper addresses the kinematics and the singularity analysis of this novel TPM and proves the effectiveness of the new design choices. The results presented here form the technical basis for the above-mentioned patent application.

Dimensional Synthesis of a Novel 3-URU Translational Manipulator Implemented through a Novel Method

“…With reference to Equations (5a) and (5b), this author demonstrated [38] that, for the LaMaViP 3-URU, the following relationships hold…”

“…The singularity analysis of the LaMaViP 3-URU has been presented in [38] and its position analysis has been solved in [42]. With reference to Figure 1, the following notations are introduced: Ox b y b z b (Px p y p z p ) is a Cartesian reference fixed to the base (to the platform), and e 1 , e 2 , and e 3 are unit vectors of the coordinate axes x b , y b , and z b (x p , y p , and z p ), respectively, and, at the same time, unit vectors of the three R-pair axes fixed to the base (to the platform).…”

“…The next section illustrates the application of this procedure to the dimensional synthesis of a TPM recently presented by the author [38], hereafter named LaMaViP 3-URU (Figure 1).…”

“…Here, a novel method for the dimensional synthesis of TPMs is presented and applied to a TPM previously proposed by this author [38]. The proposed method, which is based on Jacobians' properties, exploits the fact that TPM parallel Jacobians are block diagonal matrices [35] to overcome typical drawbacks of indices based on Jacobian properties.…”

Applying Screw Theory to Design the Turmell-Bot: A Cable-Driven, Reconfigurable Ankle Rehabilitation Parallel Robot

“…In this work, we deal with a reconfigurable low-mobility mechanism 4P-2R. A kind of lowermobility mechanism was also studied in [47,48]. The screw theory has also been applied to computing rotation centers in [49], and we used the screw theory approach applied to kinematics and statics.…”