Erik Macho

Workspaces associated to assembly modes of the 5r planar parallel manipulator

The aim of this paper is to show how it is possible to obtain for the 5R planar parallel manipulator the complete workspace associated with each solution of the direct kinematic problem or assembly mode. The workspaces associated with the different inverse kinematic problem solutions or working modes are joined and the robot moves from one to another without losing the control. An exhaustive analysis of the complete workspace and singular positions of the 5R planar parallel manipulator with two active joints is presented. Furthermore, application of these principles to path planning will be explained.

Transitions between Multiple Solutions of the Direct Kinematic Problem

The direct kinematic problem in parallel manipulators has multiple solutions that are traditionally called assembly modes. Non-singular transitions between some of these solutions have been detected and shown in the past. Cusp points have been defined as special points on the projection of the singularity curve onto the joint space that have the property of allowing such a non-singular transitions when encircling them. In this paper the authors will show that the condition for such a transition is more general. Authors also argue about the need for a differentiation between the concept of assembly mode and solution of the direct kinematic problem.

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.

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.

Design of a solar tracking parallel mechanism with low energy consumption

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.

Planning Nonsingular Transitions Between Solutions of the Direct Kinematic Problem From the Joint Space

The aim of this paper is to describe a general and systematic methodology to make controllable transitions between different solutions of the direct kinematic problem (DKP) from the joint space. This work is focused on parallel manipulators and the goal is the usage of just the input variables domain. This way, such transitions can be made controlling all the inputs simultaneously at all times. To do so, it is necessary to analyze the locus of direct kinematics singularities, where different direct kinematic solutions coalesce. It is necessary to specify which portions of such a locus specifically affect each solution. This analysis requires obtaining the locus of triple coalescence singularities. Having done this, all the information can be processed in order to obtain several maps in the joint space. Finally, it will establish the strategy on how to use these maps to connect desired solutions, including the application to a representative example.

Software Tool to Compute, Analyze and Visualize Workspaces of Parallel Kinematics Robots

The aim of this paper is to present a new software tool designed to compute and allow visualization of the different types of workspaces of parallel manipulators in the most user-friendly and efficient way. The graphical interface of this program makes it possible to define the geometrical scheme of the robot. All required parameters of the kinematic model can be set easily and quickly. Given that the workspace of a parallel manipulator is a complex entity, this CAD tool has implemented all the controls needed to visually define all the complicated parameters required to launch a workspace computation. Once the calculations are performed, the challenging task of visualizing the results has been optimized. Due to the circumstance that a workspace can be a higher than three-dimensional (3-D) mathematical entity, which cannot be graphically represented, the user can choose the specific variables (two or three) onto which to project the workspace obtained (2-D or 3-D representations). Within these surfaces and volumes, several color maps, associated with kinematic indicators, can be traced to enable the most efficient path planning of the manipulator analyzed.

A Low Energy Consumption Solar Tracker Based in Parallel Kinematics

Solar tracking devices try to increase the area exposed to direct radiation of the sun. The main drawback of these kind of devices is the energy consumed when following the sun. This work presents the design of a mechanism able to accurately follow the sun motion minimizing the energy consumption during its operation. The objective is achieved by means of a mechanism with parallel kinematics architecture.

Protein Kinematic Motion Simulation Including Potential Energy Feedback

In this article a methodology for simulating proteins function movement is presented. The procedure uses a potential energy feedback algorithm that without minizing the energy obtains succesive positions of the protein. before the simulation process, structures are normalized reducing the experimental methods produced errors. The procedure presents a low computational cost in relation to the accuracy obtained. Finally, results of the simulation for a specific protein are shown.

Computing the Configuration Space for Tracing Paths Between Assembly Modes

In this paper, the authors present a general methodology for computing the configuration space for three-degree-of-freedom parallel manipulators so that the relation between input and output variables can be easily assessed. Making use of an entity called the reduced configuration space, all solutions of the direct kinematic problem in parallel manipulators are solved. The graphical representation of this entity enables the location of the direct kinematic solutions to be analyzed so as to make use of a wider operational workspace by means of path planning. A descriptive study is presented regarding the diverse possible paths that allow changing between direct kinematic solutions, thus, enlarging the manipulator’s range of motion.