Multi-Objective Design Optimisation of a Class of Parallel Kinematic Machines

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

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