Research On High Performance Planar 2-Dof Parallel Manipulator

As a kind of advanced manufacture tool, manipulators have been applied in many fields. Through a manipulator, one can perform not only numerous simple repetitive work, but also a lot of complex work that have to be done artificially in the past, both with enhanced efficiency and improved quality. But traditional serial manipulators have the problem of joint error accumulation, low end-effector stiffness and limited overload driven capability, all of which restrict the performance of traditional serial manipulators in real applications.In order to remedy the disadvantages of serial manipulators, people invented a kind of new manipulators with structure of multiple kinematic chains—parallel manipulators. From the viewpoint of mechanisms, by manipulating the end-effector with multiple kinematic chains simultaneously, parallel manipulators have the advantages of low inertial, high stiffness and high overload driven capability, etc, which avoids the drawback of serial manipulators and makes a parallel manipulator be a potential high performance motion platform.Although the structure of multiple kinematic chains offers parallel manipulators many advantages, it increases the complexity of parallel manipulators greatly, which makes the design and real application of parallel manipulators much more difficult and restrict the performance of parallel manipulators in real applications. In this paper, with a planar 2-dof parallel manipulator, the performance improvement methods for parallel manipulators are studied from three aspects, including parameter optimal design, kinematics calibration and trajectory tracking controller design, systematically and deeply.Because of the sensitivity of the performance of parallel manipulators to the geometric value of the components, appropriate optimal design of the geometric parameters is the foundation of fulfilling full performance of parallel manipulators. But due to the inherent complex structure of multiple kinematic chains of parallel manipulators, the parameter optimal design of parallel manipulators always has the difficulties of complex singularities, too many parameters and multiple optimal objectives. In this paper, we take linear matrix inequality LMI as the mathematical tool, and formulate ordinary performance indexes of parallel manipulators by LMIs. Then with optimal method based on LMIs, the non-singularity design problem and link length optimal design problem of a planar 2-dof parallel manipulator is studied.In real applications, for the inevitable manufacture tolerances and assembling errors, there are always errors between the real values and the nominal values of kinematic parameters of parallel manipulators. So estimating the actual value of kinematic parameters of parallel manipulators by calibration procedures becomes an important means to improve the precision of parallel manipulators. In this paper, by eliminating the passive joint angles in the constraint equations, we present an elegant formulation of the constraint equations of a planar 2-dof parallel manipulator, and construct a new error function with the constraint equation. By minimizing the error function, we study the auto-calibration problem of the parallel manipulator by simulation. Furthermore, we construct the kinematic parameter error model of the parallel manipulator, and propose a two-steps iteration method for the kinematic calibration of the parallel manipulator, and study the validity of the iteration method through simulation. Furthermore, utilizing the projected tracking error of the active joints of the parallel manipulator, we define the feasible component and the infeasible component of the tracking error of the active joints, and propose an error function based on the infeasible component of the tracking errors, to calibrate the sensor zero positions of the parallel manipulator. With the proof of the robustness of the error function about the measurement error of the joint angles, the calibration precision of the error function is studied through real calibration experiments.Appropriate controller design is critical to improve the precision of parallel manipulators. First the Lagrange method for the dynamic model of parallel manipulators is summarized, and by dividing the Lagrange method into five steps, including formulating the Lagrange function, formulating the Euler-Lagrange equation, formulating the closed-loop constraints, choosing independent variables and eliminating constraint forces, we present the general procedure for modeling dynamics of parallel manipulators with Lagrange method. After formulating the dynamics of parallel manipulators as a group of differential equations with Lagrange method, we select the tracking error as state variables, and express the dynamic model by a group of state equations. With LQR method, the optimal feedback gain is calculated, and an optimal controller with forward dynamic compensation is designed. With the optimal controller, we study the trajectory tracking problem of the planar 2-dof parallel manipulator through simulation. In this paper, the joint friction compensation problem in the controller design of parallel manipulators is studied too. With coulomb friction and viscous friction, the joint friction of the planar 2-dof parallel manipulators is modeled. By transforming the dynamic model of the parallel manipulator into a group of linear equation about the friction parameters, the friction parameters are identified with least squared method. Based on the identified friction parameters, we propose an augmented PD controller with forward friction compensation, and study the validaty and superiority of the controller with real trajectory tracking control experiments.In the end of this paper, in allusion to the motion control system design of a 3-dof milling machine, we propose an open-type multiple axes controller with DSP chip TMS320LF2407A and FPGA chip EP1K30TC144-1.