V. Petuya

Synthesis and Design of a Novel 3T1R Fully-Parallel Manipulator

In this paper a new topology of four degrees-of-freedom 3T1R fully-parallel manipulator is presented, which is defined only using lower kinematic pairs. The paper starts with a complete type synthesis of different topologies of fully-parallel manipulators that can perform the so-called Schonflies motion, based on the Theory of Groups of Displacements. After imposing some practical requirements, the different possibilities of manipulators are reduced to only one topology of fully-parallel and fully-symmetrical parallel manipulator. Then, the kinematic analysis of the manipulator is shown, including the closed-form resolution of both forward and inverse position problems, the velocity and the singularity analysis. Finally, a prototype of the manipulator is presented, which is intended to be used in pick and place applications.

Educational software tools for the kinematic analysis of mechanisms

Educational software for the kinematic analysis of planar and spatial mechanisms is presented in this article. This general‐purpose kinematic software has been developed as a complement to Machine Theory lectures. The different modules integrated in the software compute and analyse various kinematic entities, which enable an advanced student to investigate the characteristics of a mechanism.

A symmetric parallel schönflies-motion manipulator for pick-and-place operations

This paper presents a new symmetric parallel Schonflies-motion generator. The design is an evolution of a previous robot with linear inputs. The complete kinematic analysis of the 4-degree-of-freedom (dof) parallel manipulator is presented. The degrees of freedom are obtained from the Group Theory, the direct and inverse position problems are solved obtaining the manipulators workspace, and the Jacobian analysis is presented. Then the isotropic configurations of the manipulator are discussed and the local dexterity map within the workspace is produced. Finally, two alternatives of a rotational mechanical device, which will increase the angular end-effector range, are proposed.

Kinematic analysis of mechanisms via a velocity equation based in a geometric matrix

In this paper, a geometrical approach is proposed to obtain a velocity equation valid for planar and spatial linkages. This equation is formed by a so called geometric matrix, and it can be found in a general and systematic way easily implemented in computer software. This procedure grants a direct inference of a kinematic property for velocities in linkages with the same topology and identical link orientation. In addition to this, a method is proposed to obtain the instantaneous degree of freedom of a mechanism in any position via the application of the geometric matrix. This also conveys a series of considerations on the detection and analysis of singular configurations. An indicator of the proximity to singularities is proposed and vectors of the motion space are found to analyse the type of singularity.

Defining Conditions for Nonsingular Transitions Between Assembly Modes

It is known that there are parallel manipulators that can perform nonsingular transitions between different assembly modes. In particular, 3-degree-of-freedom (DOF) manipulators have received primary attention related to this phenomenon. In this paper, the conditions for the existence of special points in the projection of the direct-kinematic-problem-singularity locus onto the joint space for one constant input are obtained. From these conditions, the coordinates of all cusp points can be obtained analytically. Encircling one of these cusp points, it is possible to make a nonsingular transition between two assembly modes of a parallel manipulator. Utilizing these conditions, the range for the existence of cusp points of each input value can be also determined. An extension of the concept of cusp points to the complete joint space is also performed. The procedure is applied to an RPR-2-PRR parallel manipulator that can be solved analytically. Its dimensional variables are parametrized as a 1-D function, and all results are obtained in closed form, which is a benchmark example for other procedures.

Position analysis of planar mechanisms with R -pairs using a geometrical¿iterative method

Abstract In this paper, a new method to solve the forward position problem in planar mechanisms with revolute pairs is presented. This method is based on purely geometrical concepts applying sequentially geometrical restrictions. A searching algorithm defines the order of application of these restrictions to the elements of the mechanism using some developed rules and criteria. The development of the method and its implementation in a simulation program developed by the authors is also explained. The geometric algorithm is compared with the algorithm most commonly used in kinematic analysis, i.e. the Newton–Raphson method in order to evaluate its efficiency. Several illustrative examples are presented using representative mechanisms.

Assembly Mode Changing in the Cuspidal Analytic 3-R

In this paper, the analytic 3-RPR platform studied by Wenger and Chablat in 2009 will be analyzed regarding its cuspidality condition. Many investigations have paid great attention to the cuspidality phenomena that arise for some designs of the 3-RPR parallel manipulator. Nevertheless, most of them focus on obtaining the cusp points of direct kinematic singularity curves on a section of the joint space, meaning that one of the input variables must remain constant. The authors, in this paper, obtain the locus of cusp points of the manipulator under study in a complete analytic way and in 3-D joint space. This way, the three inputs can be actuated to perform a nonsingular transition that encircles one of the curves that belong to the locus of cusp points. It will be shown that the duplicity of one of the output variables of this manipulator causes the overlapping of two different cusp points in the joint space. In order to visualize this characteristic, initially, transitions in a section of the joint space will be analyzed using, additionally, the reduced configuration space. Then, transitions in the 3-D joint space will be performed, showing that, in order to ensure a feasible nonsingular transition, it is necessary to represent the direct kinematic singularity surface and assess the evolution of the three output variables along the trajectory.

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Purpose – This paper aims to provide tools for the complete Jacobian analysis of robotic manipulators of general topology, using a comprehensive velocity equation.Design/methodology/approach – First, a modelling process is made in order to build the velocity equation using simple constraint equations: i.e. length restriction, relative motion and rigid body constraints. Then the motion space is solved, i.e. the space that spans all feasible motions of the manipulator.Findings – The velocity equation is comprehensive, i.e. it relates all kinematic variables, not only input and output. The Jacobian related to the comprehensive velocity equation is a square dimensionless matrix. This characteristic has great importance when evaluating manipulability or closeness to singularities. Employing the motion space, any kinematic entity can be studied: i.e. velocities and accelerations of any active/passive joints, screw axis, axodes, and so on. Also a comprehensive singularity analysis can be made.Research limitation...

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Solar trackers are devices that improve the efficiency of photovoltaic collectors increasing the area exposed to direct radiation of the sun. The main drawback of these kinds of devices is that they have to consume certain energy in order to move the collectors following the sun trajectory. This work presents the detailed design of a mechanism with parallel kinematics architecture able to accurately follow the sun motion, which has been designed with the aim of minimizing the energy consumption during its operation.

Computational kinematics for robotic manipulators: Jacobian problems

Purpose – The purpose of this paper is to present a step‐by‐step methodology for the design of parallel kinematic machines (PKMs), from the initial stages of the conceptual definition of a new machine to an optimum design fulfilling the complete set of design requirements.Design/methodology/approach – The methodology includes consideration of the kinematic, static and dynamic features required for the manipulator, which must all be assessed in complete industrial design. It is applied to a 4‐degrees‐of‐freedom (DOF) Schonflies motion generator for pick & place operations by way of example.Findings – The authors specify the key stages of a detailed design procedure for parallel manipulators.Originality/value – There are many publications on the development of specific robots and parallel manipulators based on their particular characteristics. However, it is relatively rare to find a paper on the general procedure with a step‐by‐step methodology applicable to any parallel manipulator.