Conference Paper

Body-oriented method for finding a linear form of the dynamic equation of fully parallel robots

Inst. of Robotics, Eidgenossische Tech. Hochschule, Zurich
DOI: 10.1109/ROBOT.1997.614371 Conference: Robotics and Automation, 1997. Proceedings., 1997 IEEE International Conference on, Volume: 2
Source: IEEE Xplore


In order to identify the dynamic parameters in nonlinear adaptive
control the robot's dynamic equation has to be written in a linear form.
Many methods have been proposed for serial robots, but for parallel
robots, the few solutions proposed so far lead to complicated equations
that are not readily usable for real-time implementation. In this paper
we propose a new method based on the virtual work principle to find a
linear form of the dynamic equation of robots. Compared to other
methods, it has the advantage that it does not need to open the closed
loop structure into a tree-structure robot. It considers rather each
body separately using its Jacobian matrix to project the forces into the
joint space of the robot. Thus, simplification can be made at the very
beginning of the modeling. This is very efficient when used to model
fully parallel robots. As an illustration, the proposed method is
applied to the 3dof DELTA parallel robot

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    • "For instance, the Lagrange–Euler formalism has been used in the works of Lee and Shah [1], Geng et al. [2] and Lebret et al. [3], Ait- Ahmed [4], Bhattacharya et al. [5] [6] and Liu et al. [7]. The principle of virtual work has been used by Tsai [8], Codourey [9] and Staicu [10] [11]. On the other hand, Newton–Euler equations have been used in the work of Sugimoto [12], Reboulet et al. [13], Ji [14], Gosselin [15] and Dasgupta et al. [16] [17]. "
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    ABSTRACT: This paper presents a method for calculating the direct and inverse dynamic models of a parallel robot with a flexible platform. The system considered in this study is a Gough–Stewart 6-DOF parallel robot however the method is general and can be used for other structures. The platform of the parallel manipulator is considered as a flexible body and modeled using distributed flexibility while the links of the legs are considered as rigid. The direct dynamic model gives the elastic and Cartesian accelerations in terms of the input torques and the current state of the system i.e. the position and velocities of both the rigid and elastic variables. The inverse dynamic model calculates the elastic accelerations and the actuator torques from the current state variables and the desired acceleration of the platform.
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    • "The component of the angular acceleration along the limb can be given according to [12] "
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    ABSTRACT: A hybrid manipulator applied to vibration isolation of the manufacturing systems is proposed in this paper. The translations and rotations of the manipulator are decoupled, so the proposed isolator can isolate vibrations with wide range of frequency, at the same time it is fully capable of adjusting the orientations of the equipments. The scheme design, inverse kinematics, workspace and dexterity are carried out in this paper. A closed form dynamic model considering the external excitations on the base platform is performed based on the Newton–Euler approach. The optimum solutions of the forces in each actuating limb are obtained by using the Moor–Penrose inverse matrix. Furthermore, a novel dynamic performance index is proposed to evaluate the estimated maximum forces in the actuating limbs; this index can help to optimally design the parameters of motor, spring and damper. In order to evaluate the performance of isolation, the displacement transmissibility and acceleration transmissibility are also analyzed. The research work provides an analytical base for the development of the novel vibration isolator.
    Full-text · Article · Jan 2012 · Journal of Manufacturing Systems
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    • "Several approaches have been applied to the dynamics analysis of parallel manipulators. They mainly can be classified into four categories: the Newton-Euler method [32] [33] [34] [35] [36] [37] [38] [39] [40] [41], Lagrangian method [42] [43] [44] [45] [46] [47] [48], Kane's method [49] [50] and virtual work principle method [51] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61] [62]. In fact, the inverse dynamics of parallel manipulators almost involve all the mechanics principles. "
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    ABSTRACT: The dynamic formulation and performance evaluation of the redundant parallel manipulator are presented in this paper. By means of the principle of virtual work and the concept of link Jacobian matrices, the inverse dynamic model of the redundant parallel manipulator is set up. It consists of six linear consistent equations with eight unknown quantities. Then, the optimum solution of the actuating torques is achieved by employing the Moore-Penrose inverse matrix. It is with minimum norm and least quadratic sum among the possible actuating torque vectors. A series of new dynamic performance indices with obvious physical meanings have been proposed in the paper. By decoupling the inverse dynamics in the exhaustive way, a novel dynamic performance index combining the acceleration, velocity and gravity terms of the dynamic equations has been presented to evaluate the dynamic characteristic of the redundant parallel manipulator. With the index, it is possible to control the performance in the different direction. The index has been applied to the dynamic characteristic evaluation of the redundant parallel manipulator in the simulation. It is general and can be used for the dynamic performance evaluation of other types of parallel manipulators.
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