Unified Parameter Modeling Of Lower Mobility Robotic Manipulators: Theory, Methodology And Application

This dissertation presents a complete theoretical package for unified parameter modeling of lower mobility robotic manipulators, and its application to the design of a novel 3-DOF PKM (Parallel Kinematic Machine) module that can be employed to configure a CNC manufacturing cell for large structural component machining in aircraft industry. The following contributions have been made.A variational representation is proposed to describe the permitted and restricted instantaneous motions of a constrained body in the configuration space. This breakthrough idea leads to the possibility to formulate various models having the same dimensions. Mainly drawing on linear algebra, supported by screw theory and Lie algebra, the wrench/twist spaces and their subspaces associated with the actuation/constraint forces and the permitted/restricted infinitesimal motions of a constrained rigid body are defined and the commutative relationships amongst these subspaces have been identified, reflecting, in general, two sides of a coin, i.e. the mobility and immobility of a constrained mechanical system. Exploiting the properties of these subspaces, a general and systematic methodology for formulating the generalized Jacobian is proposed.Based upon the generalized Jacobian, a complete package is presented that enables velocity, acceleration, accuracy, force/stiffness, and rigid body dynamics modeling of lower mobility serial and parallel manipulators to be integrated into a unified mathematical framework. The major merits can be summarized in brief.(1) Velocity modeling. A general approach to formulate dimensionally homogeneous Jacobian of lower mobility parallel manipulators having coupled translational and rotational movement capabilities is proposed, with which the heavy computational burden due to partial derivative implementations can dramatically be released.(2) Acceleration modeling. Thanks to the Lie bracket representation the Hessian matrix in an explicit and compact form is formulated in comparison with the existing influence coefficient method and"Accelerator"method available at hand.(3) Error modeling. The proposed error model allows the geometrical source errors affecting the compensatable and uncompensatable pose accuracy to be identified in an explicit manner, providing designers with an informative guideline to taking proper measures for enhancing the pose accuracy via component tolerancing and/or kinematic calibration.(4) Stiffness modeling. It has been observed that the overall stiffness matrix can be expressed as a superposition of the actuation and constraint stiffness matrices. This thereby provides the field engineers with a guideline to carry out the detailed mechanical design. Particularly, by taking 3-UPS&UP parallel mechanism as an example, an effective stiffness modeling method is presented to deal with the circumstances where the platform rigidity needs to be taken into account.(5) Rigid body dynamics. With the aid of wrench representation, the proposed dynamic model can be employed to evaluate the generalized constraint forces imposed upon the system. These forces, however, can not be achieved by the existing commercial software available on market.The proposed modeling theory and methodology have been used in the design of a novel 3-DOF parallel module, named the A3 head, which can be used to configure a manufacturing cell for large structural component machining in aircraft industry. The work in this phase involves stiffness optimization, sensitivity analysis of source errors on the uncompensatable pose accuracy, and servo motor parameter estimation. The outcome has been successfully employed for the development of a prototype machine built by Tianjin University.