Simulation and Optimisation of a Two Degree of Freedom, Planar, Parallel Manipulator
Development in pick-and-place robotic manipulators continues to grow as factory processes are streamlined. One configuration of these manipulators is the two degree of freedom, planar, parallel manipulator (2DOFPPM). A machine building company, RML Engineering Ltd., wishes to develop custom robotic manipulators that are optimised for individual pick-and-place applications. This thesis develops several tools to assist in the design process. The 2DOFPPM’s structure lends itself to fast and accurate translations in a single plane. However, the performance of the 2DOFPPM is highly dependent on its dimensions. The kinematics of the 2DOFPPM are explored and used to examine the reachable workspace of the manipulator. This method of analysis also gives insight into the relative speed and accuracy of the manipulator’s end-effector in the workspace. A simulation model of the 2DOFPPM has been developed in Matlab’s® SimMechanics®. This allows the detailed analysis of the manipulator’s dynamics. In order to provide meaningful input into the simulation model, a cubic spline trajectory planner is created. The algorithm uses an iterative approach of minimising the time between knots along the path, while ensuring the kinematic and dynamic limits of the motors and end-effector are abided by. The resulting trajectory can be considered near-minimum in terms of its cycle-time. The dimensions of the 2DOFPPM have a large effect on the performance of the manipulator. Four major dimensions are analysed to see the effect each has on the cycle-time over a standardised path. The dimensions are the proximal and distal arms, spacing of the motors and the height of the manipulator above the workspace. The solution space of all feasible combinations of these dimensions is produced revealing cycle-times with a large degree of variation over the same path. Several optimisation algorithms are applied to finding the manipulator configuration with the fastest cycle-time. A random restart hill-climber, stochastic hill-climber, simulated annealing and a genetic algorithm are developed. After each algorithm’s parameters are tuned, the genetic algorithm is shown to outperform the other techniques.