Serdar Kucuk

Comparative study of performance indices for fundamental robot manipulators

Abstract In this paper, conventional global and local indices–structural length index, manipulability measure, condition number and Global Conditioning Index (GCI)–have been examined for the workspace optimization of the sixteen fundamental robot manipulators classified by B. Huang and V. Milenkovic [Kinematics of major robot linkages, Robotics International of SME 2 (1983) 16–31]. To find the optimum link length and volumes of these robot manipulators, two design objectives have been used: maximize the workspace area covered by the robot manipulator and maximize the local indices. As an example, a three-link robot manipulator has been studied based on the above design objectives. Also, optimization results of the sixteen robot manipulators have been compared to each other and summarized in tables.

The inverse kinematics solutions of industrial robot manipulators

The inverse kinematics problem of robot manipulators is solved analytically in order to have complete and simple solutions to the problem. This approach is also called as a closed form solution of robot inverse kinematics problem. In this paper, the inverse kinematics of sixteen industrial robot manipulators classified by Huang and Milenkovic were solved in closed form. Each robot manipulator has an Euler wrist whose three axes intersect at a common point. Basically, five trigonometric equations were used to solve the inverse kinematics problems. Robot manipulators can be mainly divided into four different group based on the joint structure. In this work, the inverse kinematics solutions of SN (cylindrical robot with dome), CS (cylindrical robot), NR (articulated robot) and CC (selectively compliant assembly robot arm-SCARA, Type 2) robot manipulator belonging to each group mentioned above are given as an example. The number of the inverse kinematics solutions for the other robot manipulator was also summarized in a table.

Robot Kinematics: Forward and Inverse Kinematics

Kinematics studies the motion of bodies without consideration of the forces or moments that cause the motion. Robot kinematics refers the analytical study of the motion of a robot manipulator. Formulating the suitable kinematics models for a robot mechanism is very crucial for analyzing the behaviour of industrial manipulators. There are mainly two different spaces used in kinematics modelling of manipulators namely, Cartesian space and Quaternion space. The transformation between two Cartesian coordinate systems can be decomposed into a rotation and a translation. There are many ways to represent rotation, including the following: Euler angles, Gibbs vector, Cayley-Klein parameters, Pauli spin matrices, axis and angle, orthonormal matrices, and Hamilton s quaternions. Of these representations, homogenous transformations based on 4x4 real matrices (orthonormal matrices) have been used most often in robotics. Denavit & Hartenberg (1955) showed that a general transformation between two joints requires four parameters. These parameters known as the Denavit-Hartenberg (DH) parameters have become the standard for describing robot kinematics. Although quaternions constitute an elegant representation for rotation, they have not been used as much as homogenous transformations by the robotics community. Dual quaternion can present rotation and translation in a compact form of transformation vector, simultaneously. While the orientation of a body is represented nine elements in homogenous transformations, the dual quaternions reduce the number of elements to four. It offers considerable advantage in terms of computational robustness and storage efficiency for dealing with the kinematics of robot chains (Funda et al., 1990). The robot kinematics can be divided into forward kinematics and inverse kinematics. Forward kinematics problem is straightforward and there is no complexity deriving the equations. Hence, there is always a forward kinematics solution of a manipulator. Inverse kinematics is a much more difficult problem than forward kinematics. The solution of the inverse kinematics problem is computationally expansive and generally takes a very long time in the real time control of manipulators. Singularities and nonlinearities that make the

An off‐line robot simulation toolbox

Robotics has gained popularity in education so many engineering schools are offering robotics courses. In this study, a novel robot toolbox, “ROBOLAB” is developed for the educational users to improve the understanding of robotics fundamentals through interactive real‐time simulation. To understand manipulator movement in 3‐D space with increasing number of joints is very difficult for engineering students; because the mathematical model between joint space and physical space becomes more complex. In order to overcome this complexity, ROBOLAB based on MATLAB Graphical User Interface (GUI) includes a library for the 16 different 6 degree of freedom (6‐DOF) fundamental serial robot manipulators. The user has option to view an animation of the robot manipulators with choosing one of them or to create own GUIs based on robot project. ROBOLAB provides valuable analysis tools to students and engineering professionals in which they can compute rotation and transformation matrix, forward and inverse kinematics, and trajectory planning. Additionally, it allows user to use powerful MATLAB features such as controlling over data and formatting. In order to illustrate the features of ROBOLAB, RS cylindrical robot manipulator is given here as an example. Usage of real industrial robots in laboratory may be a very expensive way to teach robotics courses. ROBOLAB may help students to accomplish the courses and projects involving robots with minimum cost and to see 3‐D space robot applications more effectively.

Dynamics Simulation Toolbox for Industrial Robot Manipulators

A new robot toolbox for dynamics simulation based on MATLAB Graphical User Interface (GUI) is developed for educational purposes. It is built on the previous version named as ROBOLAB performing only the kinematics analysis of robot manipulators. The toolbox presented in this paper provides interactive real‐time simulation and visualization of the industrial robot manipulators dynamics based on Langrange–Euler and Newton–Euler formulations. Since most of the industrial robot manipulators are produced with six degrees of freedom (DOF) such as the PUMA 560, the Fanuc ArcMate 120iB and Stanford Arm, the library of the toolbox includes sixteen fundamental 6‐DOF robot manipulators with Euler wrist. The software can be used to interactively perform robotics analysis and off‐line programming of robot dynamics such as forward and inverse dynamics as well as to interactively teach and simulate the basic principles of robot dynamics in a very realistic way. In order to demonstrate the user‐friendly features of the toolbox much better, simulation of the NS robot manipulator (Stanford Arm) is provided as an example.

Quaternion Based Inverse Kinematics for Industrial Robot Manipulators with Euler Wrist

The major complications of inverse kinematics problem for serial robot manipulators are singularities and nonlinearities. In this context, it is important to formulize the inverse problem in a compact closed form. In this paper, we present closed form solutions of the 6-DOF industrial robot manipulators with Euler wrist using dual quaternions. The successive screw displacements in dual quaternions reduce sine/cosine-type nonlinearities, resulting in a very compact formulation. The RS, RN, and NS robot manipulators are considered as the examples of the employed method

Robot Workspace Optimization Based on a Novel Local and Global Performance Indices

In this paper, a novel performance index is introduced for the kinematics optimization of serial robot manipulators. The serial robot manipulators used in order to compare optimization results were classified as in (1). The new performance index is a combination of a manipulability measure and condition number used by previous authors. To find the optimum link lengths and volumes of these robot manipulators, two design objectives are used: maximize the workspace area covered by the robot manipulator and maximize the new local index. As examples, two spherical three-link robot manipulators are examined based on above design objectives. Finally, optimization results of these robot manipulators are obtained and compared to each other. Generally speaking, a robot manipulator structure can be subdivided into a regional structure and orientation structure. The regional structure consists of the arm (first three links), which moves the end-effector to a desired position in the workspace of the robot manipulator. The orientation structure, comprised of the last three links, rotates the end- effector to the desired orientation in the workspace. In this study, the regional structure of the robot manipulators is examined rather then the orientation structure.

Dexterous workspace optimization of an asymmetric six-degree of freedom Stewart-Gough platform type manipulator

In this paper, an asymmetric Generalized Stewart-Gough Platform (GSP) type parallel manipulator is designed by considering the type synthesis approach. The asymmetric six-Degree Of Freedom (DOF) manipulator optimized in this paper is selected among the GSPs classified under the name of 6D. The dexterous workspace optimization of Asymmetric parallel Manipulator with tEn Different Linear Actuator Lengths (AMEDLAL) subject to kinematics and geometric constraints is performed by using the Particle Swarm Optimization (PSO). The condition number and Minimum Singular Value (MSV) of homogenized Jacobian matrix are employed to obtain the dexterous workspace of AMEDLAL. Finally, the six-DOF AMEDLAL is also compared with the optimized Traditional Stewart-Gough Platform Manipulator (TSPM) considering the volume of the dexterous workspace in order to demonstrate its kinematic performance. Comparisons show that the manipulator proposed in this study illustrates better kinematic performance than TSPM.

Simulation and design tool for performance analysis of planar parallel manipulators

In this paper, a novel interactive simulation and design tool based on a MATLAB graphical user interface (GUI) is developed for the performance analysis of planar parallel manipulators (PPMs), which are a special group among the other parallel robot manipulators. The novel simulation and design tool (SIDEP) for the performance analysis of PPMs provides a suite of analysis tools allowing forward and inverse kinematics, Jacobian matrices, workspaces and singularities to be analyzed in a straightforward manner. As a simulation and design tool, SIDEP allows researchers to change the parameters such as base and end-effector coordinates the side length of the equilateral triangle moving platform and link lengths in order to interactively design their manipulators. The three-degree-of-freedom RRR and RPR PPMs are given as examples to illustrate the simulation and design principles of SIDEP.

Dimensional optimization of 6-DOF 3-CCC type asymmetric parallel manipulator

In this paper, dimensional optimization of a six-degrees-of-freedom (DOF) 3-CCC (C: cylindrical joint) type asymmetric parallel manipulator (APM) is performed by using particle swarm optimization (PSO). The 3-CCC APM constructed by defining three angle and three distance constraints between base and moving platforms is a member of 3D3A generalized Stewart–Gough platform (GSP) type parallel manipulators. The dimensional optimization purposes to find the optimum limb lengths, lengths of line segments on the base and moving platforms, attachment points of the line segments on the base platform, the orientation angles of the moving platform, and position of the end-effector in the reachable workspace in order to maximize the translational and orientational dexterous workspaces of the 3-CCC APM, separately. The dexterous workspaces are obtained by applying condition number and minimum singular values of the Jacobian matrix. The optimization results are compared with the traditional GSP manipulator for illustrating the kinematic performance of 3-CCC APM. Optimizations show that 3-CCC APM have superior dexterous workspace characteristics than the traditional GSP manipulator. Graphical Abstract