Dynamic modeling and base inertial parameters determination of a 2-DOF spherical parallel mechanism

This paper deals with the dynamic modeling and base inertial parameter determination of a general 5R 2-degree-of-freedom spherical parallel manipulator. By using a new geometric approach, inverse and forward kinematic problem are transformed to the problem of determining the intersection of two cones with common vertex. Compared to other proposed methods, this approach yields more compact and closed-form solutions. The instantaneous kinematic and acceleration problem is solved via employing the screw theory. The dynamic model is formulated by means of the principle of virtual work and the concept of link Jacobian matrices. In order to verify the proposed methods and equations, a case study is performed, in which an orthogonal 2-DOF spherical parallel manipulator, named TezGoz, is considered. Performed simulations and comparisons with a SimMechanics model show the correctness of the derived equations. Furthermore, a reduced dynamic model is obtained by determining the base inertial parameters. To do so, first the dynamic model is rewritten in a linear matrix form with respect to the inertial parameters of the mechanism, then parameters are grouped to obtain a set of independent base parameters, reducing the number of inertial parameters from 40 to 19. As a result, while maintaining the accuracy, the computational time is reduced to 63% of that of the original dynamic model. Finally, to calibrate the dynamic model, an experimental dynamic identification is performed.     

Singularity analysis of 5-RPUR parallel mechanisms (3T2R)

Singularities of parallel mechanisms are related to the regularity of certain Jacobian matrices whose rank deficiency makes the mechanisms lose their inherent rigidity. This paper presents the results of a detailed investigation of the singular configurations of 5-degree-of-freedom parallel mechanisms performing all three translations and two independent rotations. The general architecture of the mechanism—arising from the type synthesis of symmetrical 5-degree-of-freedom parallel mechanisms—is comprised of a mobile platform attached to a base through five identical revolute–prismatic–universal revolute-jointed serial kinematic chains. From the results of screw theory, it is demonstrated that the Jacobian matrix of the above mechanism is constituted by six Plücker lines, a special case of Grassmann coordinates. This channels us to use the so-called Grassmann line geometry instead of applying a classical linear algebra approach. Grassmann line geometry can be regarded as a classification of the degeneration of the Plücker line set. Moreover, six simplified designs are proposed for which their singular configurations can be predicted by means of the Grassmann line geometry. The principles of this study can also be applied to other types of symmetrical 5-degree-of-freedom parallel mechanisms.     

Optimization of Effective Sol‐Gel Parameters for the Synthesis of Mesoporous γ‐Al2O3 Using Experimental Design

Mesoporous nanocrystalline γ‐alumina was prepared by a template‐free sol‐gel method using aluminum ethoxide as precursor. Significant parameters, such as the water/aluminum ethoxide molar ratio, the pH of the solution, and the time and temperature of aging, were optimized by the Taguchi method to obtain γ‐alumina with a high surface area and pore volume. The influences of the main parameters on the catalytic performance of the prepared catalysts were investigated via dehydration of methanol to dimethyl ether in a fixed‐bed reactor. The catalysts were characterized by X‐ray diffraction, N₂ adsorption‐desorption, ammonia temperature‐programmed desorption, and scanning electron microscopy techniques. The results show that the aging temperature had a significant influence on the catalyst performance.     

Controller tuning based on optimization algorithms of a novel spherical rolling robot

This study presents the construction process of a novel spherical rolling robot and control strategies that are used to improve robot locomotion. The proposed robot drive mechanism is constructed based on a combination of the pendulum and wheel drive mechanisms. The control model of the proposed robot is developed, and the state space model is calculated based on the obtained control model. Two control strategies are defined to improve the synchronization performance of the proposed robot motors. The proportional-derivative and proportional-integral-derivative controllers are designed based on the pole placement method. The proportional-integral-derivative controller leads to a better step response than the proportional-derivative controller. The controller parameters are tuned with genetic and differential evaluation algorithms. The proportional-integral-derivative controller which is tuned based on the differential evaluation algorithm leads to a better step response than the proportional-integral-derivative controller that is tuned based on genetic algorithm. Fuzzy logics are used to reduce the robot drive mechanism motors synchronizing process time to the end of achieving a high-performance controller. The experimental implementation results of fuzzy-proportional-integral-derivative on the proposed spherical rolling robot resulted in a desirable synchronizing performance in a short time.

     

Forward kinematic problem of 5-RPUR parallel mechanisms (3T2R) with identical limb structures

This paper investigates the formulation of the forward kinematic problem of the 5-DOF parallel mechanisms performing three translation and two independent rotations with identical limb structures. The mathematical framework used in this paper is based on algebraic geometry where the forward kinematic problem is explored in a seven-dimensional kinematic space by the means of the so-called Study parameters. In this paper, the algorithms proposed for obtaining the forward kinematic expression is based on two approaches which differ by their concept of eliminating passive variables. The first one is based on the application of the so-called resultant method and the second one, as a novel approach referred to as linear implicitization algorithm, uses an elimination procedure based on solving several systems of linear equations. The forward kinematic problem is solved using the homotopy continuation and it is revealed that it has 1680 finite solutions. Moreover, the forward kinematic problem is studied in three-dimensional Euclidean space where a class of simplified designs are proposed which admit a simpler formulation for the forward kinematic problem. Finally, based on the simplified designs, for a nearly general design a univariate expression of degree 220 is obtained.