Raffaele Di Gregorio

Mobility Analysis of the 3-UPU Parallel Mechanism Assembled for a Pure Translational Motion

The occurrence of singular configurations in parallel mechanisms must be avoided during motion since the actuators cannot control motion eyen in the neighborhood of these configurations. As a consequence, the knowledge of the singular configurations of the mechanism is important for control purposes, for singularity-free path planning, and also represents basic information for the synthesis of a desired mechanism workspace free from singularities. In this paper the mobility analysis of the 3-UPU parallel mechanism assembled for obtaining a pure translation motion of the output platform is performed and both translation and rotation singularity loci are presented in analytic form and their geometric interpretation is given.

A new parallel wrist using only revolute pairs: the 3-RUU wrist

Only one parallel wrist with three equal legs containing just revolute pairs has been already presented in the literature. This parallel wrist is overconstrained, i.e., it involves three degrees of freedom required to orientate the end effector by using repetitions of constraints. The overconstrained mechanisms have the drawback of jamming or undergoing high internal loads when geometric errors occur. This paper presents a new parallel wrist, named 3-RUU wrist. The 3-RUU wrist is not overconstrained. It has three equal legs just involving revolute pairs and actuators adjacent to the frame and uses an architecture (3-RUU) already employed to obtain manipulators that make the end effector translate. The 3-RUU wrist kinematic analysis is addressed. This analysis shows that the new parallel wrist can reach singular configurations (translation singularities) in which the spherical constraint between end effector and frame fails. The singularity condition that makes finding all the 3-RUU wrist singular configurations possible is written in explicit form and geometrically interpreted.

A new family of spherical parallel manipulators

In the literature, 3-RRPRR architectures were proposed to obtain pure translation manipulators. Moreover, the geometric conditions, which 3-RRPRR architectures must match, in order to make the end-effector (platform) perform infinitesimal (elementary) spherical motion were enunciated. The ability to perform elementary spherical motion is a necessary but not sufficient condition to conclude that the platform is bound to accomplish finite spherical motion, i.e. that the mechanism is a spherical parallel manipulator (parallel wrist). This paper demonstrates that the 3-RRPRR architectures matching the geometric conditions for elementary spherical motion make the platform accomplish finite spherical motion, i.e. they are parallel wrists (3-RRPRR wrist), provided that some singular configurations, named translation singularities, are not reached. Moreover, it shows that 3-RRPRR wrists belong to a family of parallel wrists which share the same analytic expression of the constraints which the legs impose on the platform. Finally, the condition that identifies all the translation singularities of the mechanisms of this family is found and geometrically interpreted. The result of this analysis is that the translation singularity locus can be represented by a surface (singularity surface) in the configuration space of the mechanism. Singularity surfaces drawn by exploiting the given condition are useful tools in designing these wrists.

The 3-RRS wrist: A new, simple and non-overconstrained spherical parallel manipulator

Orientating a rigid body without changing its position is required in many technical applications. This manipulation task is accomplished by manipulators (spherical manipulators) that are just able to make the end effector move according to controlled spherical motions. Spherical manipulators can be either serial or parallel. Parallel architectures are usually more stiff and precise than the serial ones, whereas their structures are more complex than the serial ones. This paper presents a new three-equal-legged spherical parallel manipulator named the 3-RRS wrist. The 3-RRS wrist is not overconstrained and exhibits a simple architecture employing just three passive revolute pairs, three passive spherical pairs and three actuated revolute pairs adjacent to the frame. The kinematic analysis of the 3-RRS wrist is addressed and fully solved. Finally, its singularity conditions are written in explicit form and discussed. The results of this analysis lead to the conclusion that the new manipulator has only two types of singularities both easy to be identified with geometric reasoning.

Kinematics of the 3-UPU wrist

Abstract Recently, it has been shown that a parallel mechanism architecture, called 3-UPU and used for translational manipulators, can be employed to obtain manipulators able to make the end effector perform infinitesimal spherical motions. The possibility of performing infinitesimal spherical motions is a necessary but not sufficient condition to guarantee that the end effector performs a finite spherical motion, i.e., the manipulator is a parallel wrist. In this paper it is demonstrated that the 3-UPU architecture, can be employed to obtain parallel wrists, named 3-UPU wrists. Moreover, it is shown that the 3-UPU wrists may reach singular configurations in which the spherical constraint between the end effector and the frame fails. Finally, the singularity condition, that makes it possible to find all the 3-UPU wrist’s singular configurations, is written in explicit form and is geometrically interpreted.

Dynamics of a Class of Parallel Wrists

This paper presents a dynamic model of parallel wrists with all links constrained to have a spherical motion with the same center. The model can also be applied to serial wrists. The model, based on Lagrangian formulation of dynamics, exploits the feature that all the links have the same fixed point. Three parameters defining the platform orientation are used as generalized coordinates. This choice allows the use of the generalized inertia matrix (GIM) appearing in the model to calculate effective dynamic performance indices proposed in a previous paper. The model can solve both the direct and the inverse dynamic problems. It also contains the Jacobian matrix useful to characterize the kinematic behavior of parallel manipulators. By the model it is shown that the best performances are reached in the workspace regions where the manipulator has a good kinematic and dynamic isotropy, whereas the incidence of nonlinear forces on performances is relevant at high end-effector speed. A numerical example is provided.

Singularity-locus expression of a class of parallel mechanisms

In parallel mechanisms, singular configurations (singularities) have to be avoided during motion. All the singularities should be located in order to avoid them. Hence, relationships involving all the singular platform poses (singularity locus) and the mechanism geometric parameters are useful in the design of parallel mechanisms. This paper presents a new expression of the singularity condition of the most general mechanism (6-6 FPM) of a class of parallel mechanisms usually named fully-parallel mechanisms (FPM). The presented expression uses the mixed products of vectors that are easy to be identified on the mechanism. This approach will permit some singularities to be geometrically found. A procedure, based on this new expression, is provided to transform the singularity condition into a ninth-degree polynomial equation whose unknowns are the platform pose parameters. This singularity polynomial equation is cubic in the platform position parameters and a sixth-degree one in the platform orientation parameters. Finally, how to derive the expression of the singularity condition of a specific FPM from the presented 6-6 FPM singularity condition will be shown along with an example.

A New Algorithm Based on Two Extra-Sensors for Real-Time Computation of the Actual Configuration of the Generalized Stewart-Gough Manipulator

It is well known that the direct position analysis of fully-parallel manipulators provides more than one solution, i.e., more than one configuration of the mechanism is possible for a given set of the actuated variables of motion. Extra information is, thus, necessary to find the actual configuration of the manipulator. This paper presents a new algorithm for the real-time computation of the actual configuration of the generalized Stewart-Gough manipulator, also known as 6-6 fully-parallel manipulator with general geometry. The proposed algorithm makes use of two extra rotary sensors in addition to five out of the six sensors normally implemented in the servosystems of the manipulator. A one-to-one correspondence between the sensor measurements and the manipulator configuration is provided. With respect to other algorithms recently presented in the literature, the proposed method greatly reduces the computational burden. Finally a case study shows the effectiveness of the proposed procedure.

Kinematics of the translational 3-URC mechanism

The use of less than six degrees of freedom (dof) mechanisms instead of six-dof ones is always recommended when the application makes it possible, since their architectures and control are simpler to manufacture and implement respectively. Three-dof mechanisms constitute an important subset of less-than-six-dof mechanisms, since either translational or spherical motion can be obtained through three-dof spatial mechanisms and many industrial applications require the only translational or spherical motion. This paper presents a new translational parallel mechanism (TPM), named translational 3-URC. The new mechanism belongs to the parallel architectures with 3-URC topology, which contain another architecture that is a spherical parallel wrist. The proposed TPM is not overconstrained and has three equal legs whose kinematic pairs are three revolute pairs and one passive cylindrical pair per leg. Its actuated pairs are three revolute pair located on the frame. The position and velocity analyses of the translational 3-URC will be addressed and solved. Its singularity conditions will be written in explicit form and geometrically interpreted.

On the Modeling of Passive Motion of the Human Knee Joint by Means of Equivalent Planar and Spatial Parallel Mechanisms

Recent literature in biomechanics has demonstrated that motion of the human knee joint in virtually unloaded conditions is guided in a single and complex path by the passive structures of the joint alone. It has been deduced that the joint behaves as a single degree of freedom mechanism. Early models, dated on beginning of this century, showed this in the sagittal plane only. The three dimensional motion has been recently modelled by means of equivalent parallel mechanisms, based also on experimental observations on knee specimens of two separate frictionless contacts and three isometric ligament fibres.The model of the joint is a key tool for a deeper understanding of the knee motion and the design of reliable and efficient prostheses. It also provides useful information for the planning of surgical intervention on the basic structures of the knee.The progress of this modelling is reported in this paper. A medical and biomechanical rationale for these studies is provided, together with a number of relevant publications. The pioneering planar four-bar linkage has been initially advanced to a single degree of freedom equivalent spatial mechanism characterised by plane-to-sphere contacts. The closure equations for this mechanism have been progressively simplified. Extensions to more complex articular surfaces have been also performed. The results reported for all these models demonstrate that the original model assumptions were valid and that refinements in articular surface descriptions are justified to a certain extent.