Design, Analysis, and Fabrication of a Five-Axis Hybrid Kinematics Machine Tool

Student thesis: Doctoral Thesis


Hybrid kinematics machines have been proposed to integrate the advantages of both serial and parallel kinematics machines. This thesis proposed a novel five-axis machine tool with a hybrid kinematics composed by conjugating two non-symmetric planar 3PRR parallel kinematics mechanisms. A prototype of the proposed machine was built and experimental tests were performed on the prototype. The inverse and forward kinematics of the machine was formulated. Quaternions were used to avoid the formulation singularity in the forward kinematics. To improve the performance of the machine, the workspace, the minimum eigenvalue of the stiffness matrix, and the stiffness condition number were optimized in a multi-objective optimization scheme based on the weighted sum and Pareto approaches by using a genetic algorithm. The dynamics of the mechanism used in the machine was modeled by considering both rigid body and flexible body assumptions. The rigid body dynamics was solved by using coordinate partitioning and velocity transformation methods. The flexible body dynamics was modeled based on the floating reference frame formulation. The Euler-Bernoulli beams were used to evaluate the elastic displacements and the natural frequencies. Since one of the mechanisms used is working against the gravity, a gravity compensator using torsional spring were developed. A statics-based method was proposed to find the required compensation torques. To improve the accuracy of the machine, an external kinematic calibration using a laser tracker was performed. A variant of nonlinear least squares and an iterative linear least squares were used to estimate the kinematic parameters. To get an accurate dynamic model of the mechanism, a dynamic parameter identification method which considers the varying friction on the active prismatic joints was developed. The physical feasibility was maintained by introducing the bounds of the parameters. To reduce the contouring errors, smoother motion profiles and some control schemes were proposed. Some PID-based and model-based control architectures were built, implemented, and evaluated.
Date of AwardDec 2018
Original languageAmerican English
SupervisorBashar El Khasawneh (Supervisor)


  • Hybrid Kinematics

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