Thesis (Ph.D.)--McMaster University, 2005. / Supervisor: M. A. Elbestawi. Includes bibliographical references (leaves 183-204).

This paper presents the research and development of a 3-legged micro Parallel Kinematic Manipulator (PKM) for positioning in micro-machining and assembly operations. The structural characteristics associated with parallel manipulators are evaluated and the PKMs with translational and rotational movements are identified. Based on these identifications, a hybrid 3-UPU (Universal Joint-Prismatic Joint-Universal Joint) parallel manipulator is designed and fabricated. The principles of the operation and modeling of this micro PKM is largely similar to a normal size Stewart Platform (SP). A modular design methodology is introduced for the construction of this micro PKM. Calibration results of this hybrid 3-UPU PKM are discussed in this paper. / Singapore-MIT Alliance (SMA)

The thesis is about design and analysis of a PKM with 3 DOF. The new PKM is designed as a machine tool in various applications in manufacturing. The PKM is optimized based on the developed stiffness model. Kinematics and dynamics of the new PKM is also modeled and simulated. / UOIT

The aim of using parallel kinematic motion systems as an alternative of conventional machine tools for precision machining has raised the demands made on the accuracy of identification of the geometric parameters that are necessary for the kinematic transformation of the motion variables. The accuracy of a parallel manipulator is not only dependent upon an accurate control of its actuators but also upon a good knowledge of its geometrical characteristics. As the platform's controller determines the length of the actuators according to the nominal model, the resulted pose of the platform is inaccurate. One way to enhance platform accuracy is by kinematic calibration, a process by which the actual kinematic parameters are identified and then implemented to modify the kinematic model used by the controller. The first and most general valuation criterion for the actual calibration approaches is the relative improvement of the motion accuracy, eclipsing the other aspects to pay for it. The calibration outlay has been underestimated or even neglected for a long time. The scientific value of the calibration procedure is not only in direct proportion to the achieved accuracy, but also to the calibration effort. These demands become particularly stringent in case of the calibration of hexapods of the so-called simple design. The objectives of the here proposed new calibration procedure are based on the deficits mentioned above under the special requirements due to the circumstances of the simple design-concept. The main goals of the procedure can be summarized in obtaining the basics for an automated kinematic calibration procedure which works efficiently, quickly, effectively and possibly low-cost, all-in-one economically applied to the parallel kinematic machines. The problem will be approached systematically and taking step by step the necessary conclu-sions and measurements through: Systematical analysis of the workspace to determine the optimal measuring procedure, measurements with automated data acquisition and evaluation, simulated measurements based on the kinematic model of the structure and identifying the kinematic parameters using efficient optimization algorithms. The presented calibration has been successfully implemented and tested on the hexapod of simple design `Felix' available at the IWM, TU Dresden. The obtained results encourage the application of the procedure to other hexapod structures.

Parallel Kinematic Mechanisms (PKMs) are well suited for high-accuracy applications such as meso-milling. However, drawbacks such as limited platform tilting angle and high configuration dependency of stiffness often limit their usage. In this Thesis, a new six degree-of-freedom (dof) PKM architecture based on a 3×PPRS topology is proposed, in order to address these problems. The new PKM is presented, and its inverse kinematics and Jocobian matrix are derived. The kinematic relations are incorporated into MATLAB to calculate the workspace of the PKM. The stiffness of the new PKM is obtained using Finite Element Analysis (FEA), and configuration dependency of stiffness is investigated. The proposed new mechanism is compared with three similar existing 6-dof PKMs, and it is shown that the new PKM exhibits higher stiffness. Lastly, three meso-Milling Machine Tool prototypes were designed and built. In particular, Prototype III is based on the new mechanism.

Parallel Kinematic Mechanisms (PKMs) are well suited for high-accuracy applications such as meso-milling. However, drawbacks such as limited platform tilting angle and high configuration dependency of stiffness often limit their usage. In this Thesis, a new six degree-of-freedom (dof) PKM architecture based on a 3×PPRS topology is proposed, in order to address these problems. The new PKM is presented, and its inverse kinematics and Jocobian matrix are derived. The kinematic relations are incorporated into MATLAB to calculate the workspace of the PKM. The stiffness of the new PKM is obtained using Finite Element Analysis (FEA), and configuration dependency of stiffness is investigated. The proposed new mechanism is compared with three similar existing 6-dof PKMs, and it is shown that the new PKM exhibits higher stiffness. Lastly, three meso-Milling Machine Tool prototypes were designed and built. In particular, Prototype III is based on the new mechanism.

One of the main advantages of the Gantry-Tau machine is a large accessible workspace\footprint ratio compared to many other parallel machines. The Gantry-Tau improves this ratio further by allowing a change of assembly mode without internal link collisions or collisions between the links and the moving TCP platform. In this Thesis some of the features of the Gantry-Tau structure are described and results are presented from the analysis of the kinematic, elastostatic and elastodynamic properties of the PKM. However, the optimal kinematic, elastostatic and elastodynamic design parameters of the machine are still difficult to calculate and this thesis introduces a multi-objective optimisation scheme based on the geometric approach for the workspace area, unreachable area, joint angle limitations and link collisions as well as the functional dependencies of the elements of the static matrix and the Laplace transform to define the first resonance frequency and Cartesian and torsional stiffness. The method to calculate the first resonance frequency assumes that each link and universal joint can be described by a mass-springdamper model and calculates the transfer function from a Cartesian (TCP) force or torque to Cartesian position or orientation. The geometric methods involve the simple geometric shapes (spheres, circles, segments, etc) and vectors. The functional dependencies are based on the properties between the kinematic parameters. These approaches are significantly faster than analytical methods based on the inverse kinematics or the general Finite Elements Method (FEM). The reconfigurable Gantry-Tau kinematic design obtained by multi-objective optimisation gives the following features: • Workspace/footprint ratio more than 3.19. • First resonance frequency greater than 48 Hz. • Lowest Cartesian stiffness in the workspace 5N/μm. • The unreachable space in the middle of the workspace is not detected. • No link collisions. The results show that by careful design of the PKM, a collision free workspace without the unreachable area in the middle can be achieved. High stiffness and high first resonance frequency are important parameters for the the Gantry-Tau when used in industrial applications, such as cutting, milling and drilling of steel or aluminium and pick-and-place operations. These applications require high static and dynamic accuracy in combination with high speed and acceleration. The optimisation parameters are the support frame lengths, actuator positions,endeffector kinematics and the robot’s arm lengths. Because of the fast computational speed of the geometric approaches and computational time saving of the methods based on the functional dependency, they are ideal for inclusion in a design optimisation framework, normally a nonlinear optimisation routine. In this Thesis the evolutionary algorithm based on the complex search method is used to optimise the 3-DOF Gantry-Tau. The existing lab prototype of this machine was assembled and completed at the University of Agder

Der Vortrag verdeutlicht die Möglichkeiten der Mathcad-Funktionen "Minimieren" bzw. "Maximieren" durch ein komplexes Beispiel aus dem Gebiet der parallelkinematischen Robotik. Innerhalb eines technologisch geforderten Arbeitsbereiches werden durch Auswertung der Vorwärts- und Rückwärtsinformation Bewertungskriterien erfasst und anschaulich dargestellt. Durch eine geeignete Formulierung mit den "Programmier"-Werkzeugen von Mathcad kann die Bewertung in einer Funktion über den gesamten Arbeitsraum automatisiert aufgerufen werden. Diese Aufbereitung gestattet die Anwendung der "Maximieren"-Funktion auf die Arbeitseigenschaften der Maschine durch Variation der kinematischen Abmessungen. Das Ergebnis der Optimierung sind die Maße des mechanischen Führungsgetriebes.

One of the main advantages of the Gantry-Tau machine is a large accessible workspace\footprint ratio compared to many other parallel machines. The Gantry-Tau improves this ratio further by allowing a change of assembly mode without internal link collisions or collisions between the links and the moving TCP platform. In this Thesis some of the features of the Gantry-Tau structure are described and results are presented from the analysis of the kinematic, elastostatic and elastodynamic properties of the PKM. However, the optimal kinematic, elastostatic and elastodynamic design parameters of the machine are still difficult to calculate and this thesis introduces a multi-objective optimisation scheme based on the geometric approach for the workspace area, unreachable area, joint angle limitations and link collisions as well as the functional dependencies of the elements of the static matrix and the Laplace transform to define the first resonance frequency and Cartesian and torsional stiffness. The method to calculate the first resonance frequency assumes that each link and universal joint can be described by a mass-springdamper model and calculates the transfer function from a Cartesian (TCP) force or torque to Cartesian position or orientation. The geometric methods involve the simple geometric shapes (spheres, circles, segments, etc) and vectors. The functional dependencies are based on the properties between the kinematic parameters. These approaches are significantly faster than analytical methods based on the inverse kinematics or the general Finite Elements Method (FEM). The reconfigurable Gantry-Tau kinematic design obtained by multi-objective optimisation gives the following features: • Workspace/footprint ratio more than 3.19. • First resonance frequency greater than 48 Hz. • Lowest Cartesian stiffness in the workspace 5N/μm. • The unreachable space in the middle of the workspace is not detected. • No link collisions. The results show that by careful design of the PKM, a collision free workspace without the unreachable area in the middle can be achieved. High stiffness and high first resonance frequency are important parameters for the the Gantry-Tau when used in industrial applications, such as cutting, milling and drilling of steel or aluminium and pick-and-place operations. These applications require high static and dynamic accuracy in combination with high speed and acceleration. The optimisation parameters are the support frame lengths, actuator positions,endeffector kinematics and the robot’s arm lengths. Because of the fast computational speed of the geometric approaches and computational time saving of the methods based on the functional dependency, they are ideal for inclusion in a design optimisation framework, normally a nonlinear optimisation routine. In this Thesis the evolutionary algorithm based on the complex search method is used to optimise the 3-DOF Gantry-Tau. The existing lab prototype of this machine was assembled and completed at the University of Agder

Thesis (Ph.D.(Mechanical Engineering))--University of Pretoria, 2003. / Summaries in Afrikaans and English. Includes bibliographical references.