A Three Degree of Freedom Parallel Manipulator with Only Translational Degrees of Freedom
Stamper, R. E.
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In this dissertation, a novel parallel manipulator is investigated. The manipulator has three degrees of freedom and the moving platform is constrained to only translational motion. The main advantages of this parallel manipulator are that all of the actuators can be attached directly to the base, closed-form solutions are available for the forward kinematics, the moving platform maintains the same orientation throughout the entire workspace, and it can be constructed with only revolute joints. Closed-form solutions for both the forward and inverse kinematics problems are presented. It is shown that the inverse kinematics problem has up to four real solutions, and the forward kinematics problem has up to 16 real solutions. The Jacobian matrix for the manipulator is also developed, and used to identify singular poses of the manipulator, where the manipulator instantaneously gains or loses a degree of freedom. The manipulator workspace volume as a function of link lengths and leg orientation is determined using the Monte Carlo method. A procedure for characterizing the quality of the workspace is also developed. Using these results, optimization studies for maximum workspace volume and for well-conditioned workspace volume are conducted. The objective function for the well-conditioned optimization study is defined as the integration of the reciprocal of the condition number of the Jacobian matrix over the workspace volume, and named the global condition index. Three different models are developed for the manipulator dynamics, with numerical simulations presented for all three models. The first model is based upon the application of the Newton-Euler equations of motion used in conjunction with the Jacobian matrix to map the inertial and gravitational loadings of the moving platform to the actuators. The second model was developed to give a more complete characterization of the dynamics, and is based upon the Lagrangian multiplier approach. The third model neglects the highly coupled nature of the manipulator and models each input link individually. This model is developed for use with single- input single-output type controllers. A prototype was fabricated to demonstrate this manipulator. Three controllers are developed and tested on the prototype, where each type of control tested relied on different characterizations of the manipulator dynamics. The three controllers are a PID controller, a computed torque controller, and an iterative learning controller. The research presented in this dissertation establishes this parallel manipulator as a viable robotic device for three degree of freedom manipulation. The manipulator offers the advantages associated with other parallel manipulators, such as light weight construction; while avoiding some of the traditional disadvantages of parallel manipulators such as the extensive use of spherical joints and coupling of the platform orientation and position.