Genetic and hybrid algorithms for optimization of non-singular 3PRR planar parallel kinematics mechanism for machining application

SUMMARYThis paper proposes a special non-symmetric topology of a 3PRR planar parallel kinematics mechanism, which naturally avoids singularity within the workspace and can be utilized for hybrid kinematics machine tools. Subsequently, single-objective and multi-objective optimizations are conducted to improve the performance. The workspace area and minimum eigenvalue, as well as the condition number of the homogenized Cartesian stiffness matrix across the workspace, have been chosen as the objectives in the optimization based on their relevance to the machining application. The single-objective optimization is conducted by using a single-objective genetic algorithm and a hybrid algorithm, whereas the multi-objective optimization is conducted by using a multi-objective genetic algorithm, a weighted sum single-objective genetic algorithm, and a weighted sum hybrid algorithm. It is shown that the single-objective optimization gives superior value in the optimized objective, while sacrificing the other objectives, whereas the multi-objective optimization compromises the improvement of all objectives by providing non-dominated values. In terms of the algorithms, it is shown that a hybrid algorithm can either verify or refine the optimal value obtained by a genetic algorithm.

A Non-Linear Stiffness Model for Serial and Parallel Manipulators

The paper presents a methodology to enhance the stiffness analysis of serial and parallel manipulators with passive joints. It directly takes into account the loading influence on the manipulator configuration and, consequently, on its Jacobians and Hessians. The main contributions of this paper are the introduction of a non-linear stiffness model for the manipulators with passive joints, a relevant numerical technique for its linearization and computing of the Cartesian stiffness matrix which allows rank-deficiency. Within the developed technique, the manipulator elements are presented as pseudo-rigid bodies separated by multidimensional virtual springs and perfect passive joints. Simulation examples are presented that deal with parallel manipulators of the Ortholide family and demonstrate the ability of the developed methodology to describe non-linear behaviour of the manipulator structure such as a sudden change of the elastic instability properties (buckling).

Stiffness analysis and comparison of a Biglide parallel grinder with alternative spatial modular parallelograms

SUMMARYThis paper deals with the stiffness modeling, analysis and comparison of a Biglide parallel grinder with two alternative modular parallelograms. It turns out that the Cartesian stiffness matrix of the manipulator has the property that it can be decoupled into two homogeneous matrices, corresponding to the translational and rotational aspects, through which the principal stiffnesses and the associated directions are identified by means of the eigenvalue problem, allowing the evaluation of the translational and rotational stiffness of the manipulator either at a given pose or the overall workspace. The stiffness comparison of the two alternative Biglide machines reveals the (dis)advantages of the two different spatial modular parallelograms.

Stiffness Modeling of Robotic-Manipulators Under Auxiliary Loadings

The paper focuses on the extension of the virtual-joint-based stiffness modeling technique for the case of different types of loadings applied both to the robot end-effector and to manipulator intermediate points (auxiliary loading). It is assumed that the manipulator can be presented as a set of compliant links separated by passive or active joints. It proposes a computationally efficient procedure that is able to obtain a non-linear force-deflection relation taking into account the internal and external loadings. It also produces the Cartesian stiffness matrix. This allows to extend the classical stiffness mapping equation for the case of manipulators with auxiliary loading. The results are illustrated by numerical examples.

Stability of Manipulator Configuration Under External Loading

The paper is devoted to the analysis of robotic manipulator behavior under internal and external loadings. The main contributions are in the area of stability analysis of manipulator configurations corresponding to the loaded static equilibrium. In contrast to other works, in addition to usually studied the end-platform behavior with respect to the disturbance forces, the problem of configuration stability for each kinematic chain is considered. The proposed approach extends the classical notion of the stability for the static equilibrium configuration that is completely defined the properties of the Cartesian stiffness matrix only. The advantages and practical significance of the proposed approach are illustrated by several examples that deal with serial kinematic chains and parallel manipulators. It is shown that under the loading the manipulator workspace may include some specific points that are referred to as elastostatic singularities where the chain configurations become unstable.

Decoupling of the Cartesian Stiffness Matrix: A Case Study on Accelerometer Design

The 6 × 6 Cartesian stiffness matrix obtained through finite element analysis for structures designed with material and geometric symmetries may lead to unexpected coupling that stems from discretization error. Hence, decoupling of the Cartesian stiffness matrix becomes essential for design and analysis. This paper reports a numerical method for decoupling the Cartesian stiffness matrix, based on screw theory. With the aid of this method, the translational and rotational stiffness matrices can be analyzed independently. The mechanical properties of the decoupled stiffness submatrices are investigated via their associated eigenvalue analyses. The decoupling technique is applied to the design of two accelerometer layouts, uniaxial and biaxial, with what the authors term simplicial architectures. The decoupled stiffness matrices reveal acceptable compliance along the sensitive axes and high off-axis stiffness.