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DINAME 2017
XVII International Symposium on Dynamic Problems of Mechanics
DYNAMIC MODELLING AND IDENTIFICATION OF A PLANAR PKM WITH SEVERAL LEVELS OF KINEMATIC REDUNDANCIES
Submission Author:
Maíra Martins da Silva , SP
Co-Authors:
João Vitor de Carvalho Fontes, João Cavalcanti Santos, Hiparco Lins Vieira, Maíra Martins da Silva
Presenter: Maíra Martins da Silva
doi://10.26678/ABCM.DINAME2017.DIN17-0101
Abstract
The performance of parallel kinematic manipulators may be enhanced by the use of kinematic redundancies since they promote a significant reduction in the singularities and homogenization on the actuation forces [1]. Kinematic redundancy can be implemented by the introduction of extra active joints in a kinematic chain. Because of this, the inverse kinematic problem presents infinite solutions, i.e. there are infinite possible joint parameters for a single end effector's pose. The full capability of several levels of kinematic redundancies can only be assessed by appropriate motion planning and by the design of efficient model-based control strategies. Both methodologies rely on the use of validated kinematic and dynamic models. This work treats the dynamic modeling and identification of a planar parallel kinematic manipulator (PKM) with several levels of kinematic redundancies, the 3PRRR. Figure 1a illustrates a scheme of the geometry of the 3PRRR. As commonly used in the field of parallel robots, the letter R corresponds to revolute joints, the letter P corresponds to prismatic joints, the underline letter to actuated joints and the number in front of the name refers to the number of kinematic chains. The end-effector of this planar manipulator is considered a rigid body that can move in plane, yielding a system with three DOFs. The actuation of these DOFs is done by six servomotors: three moving three linear guides (P) and three moving links (R). In this way, this PKM presents three levels of kinematic redundancies. A 3PRRR prototype, depicted in Fig. 1b, was built at São Carlos School of Engineering – University of São Paulo. The actuators are Maxon DC motors connected to digital positioning controllers. The connection between these controllers is via CAN protocol. The human machine interface is implemented in two ways: (i) via Matlab and USB communication and (ii) via Matlab/Simulink and DSpace/CAN communication. In order to accomplish the main objective of this work, detailed kinematic and dynamic models are employed [2]. Based on the geometric description of the prototype and its constraints (see Fig. 1a), forward and inverse kinematic models are been derived. Using the Euler-Lagrange formalism and the Lagrange multiplier technique to account for the kinematic constraints, the equations of motion are derived. The Inverse Dynamic model can be used to evaluate the required forces and torques to perform pre-defined end-effector’s movements. The Forward Dynamic model can be employed to assess the resulting end-effector’s movement for a given set of forces and torques. These equations can be integrated using the Backward Differential Formula (BDF). The estimation of the parameters used in the dynamic models is mandatory for deriving validated models that can be used for motion planning and model-based control strategies. So, an identification procedure based on an optimization problem is proposed to the identification of some dynamic parameters such as masses, inertias, friction coefficients, among others. The selection of the excitation trajectories play an important role in the identification procedure [3]. Excitation trajectories based on finite Fourier series have been successfully employed to the identification of dynamic parameters of PKMs and it is also exploited in this work. The optimization procedure aims to minimize the difference between the experimental and numerical data by identify the dynamic parameters correctly. This nonlinear problem can be solved using several nonlinear optimization algorithms. The comparison between the experimental and numerical data demonstrate the effectiveness of the employed methodology.
Keywords
parallel kinematic manipulators, System Identification, kinematic redundancy
