Multibody Dynamics of Nonsymmetric Planar 3PRR Parallel Manipulator with Fully Flexible Links

Abstract

This paper presents the implementation of the floating frame of reference formulation to model the flexible multibody dynamics of a nonsymmetric planar 3PRR parallel manipulator. All of the links, including the moving platform, of the manipulator under study are assumed flexible whereas the joints are assumed rigid. Using the Euler-Bernoulli beam, the flexibility of the links is modeled by using the Rayleigh-Ritz and finite element approximations. In both approximations, fixed-free boundary conditions are applied to the elastic coordinates of the links. These boundary conditions enable the evaluation of the elastic displacement at a link tip coincident with the end-effector of the manipulator which is of interest in the high precision robotics application. Both the approximations were compared by applying two different types of loads to the manipulator. It is shown that the elastic displacements obtained by using both the approximations have an agreement with a slight difference in the magnitude. In addition, the sensitivity analysis shows that the rigidity of the manipulator is much affected by the in-plane depth of the manipulator links’ cross section.

Control Method of Flexible Manipulator Servo System Based on a Combination of RBF Neural Network and Pole Placement Strategy

“…The flexibility of a flexible load is equivalent to the flexibility of a flexible manipulator. According to the literature [25,26], the flexible load can be equal to the Euler-Bernoulli flexible beam model. where T m , T l , T a represent the electromagnetic motor torque, the external torque of the load side, the input torque of the flexible load; w(x, t) represents the deformation of the flexible load; θ m , θ represent the rotation angle of motor side, and the rotation angle of flexible load; XOY, x 0 Oy 0 represent the static coordinate and the moving coordinate; mg represents the gravity.…”

“…Besides, the input torque is closely associated with the gravity term. In this paper, according to Equation (25), Equation (30), and Equation ( 31), the relationship between input torque and time under different manipulators' lengths is respectively calculated in two conditions, as shown in Figure 8. One of the cases ignores the gravitational factor, and the other case considers the gravitational factor.…”

Towards a More Robust Non-Rigid Robotic Joint

“…where d(θ) is introduced to model the dead-zone and B(ω) to model the viscous friction. d(θ) is defined by Equation ( 6), where −θ d and θ d are the dead zone left and right limits, as illustrated in Figure 4, while B(ω) is defined by Equation (7).…”

“…Despite the evolutionary effort for using flexible and more sophisticated solutions for the market [2][3][4][5][6][7], it is not yet very easy to find solutions in mature states with which to explore and perform experimental work, as Hoffman et al [8] report. Even so, there are some works that should be mentioned, since they present varied solutions.…”

Nonprehensile Manipulation of Parts on a Horizontal Circularly Oscillating Platform with Dynamic Dry Friction Control

“…Parts on a horizontal platform can be moved by various means. For example, this can be performed by using parallel manipulators [ 1 , 2 , 3 , 4 ] by applying piezoelectric or electromagnetic actuated planar micromanipulators [ 5 , 6 , 7 , 8 ], by pushing with robot end-effectors [ 9 , 10 , 11 ], by transporting with devices which move together with the parts to be displaced (e.g., mobile robots) [ 12 , 13 , 14 ], by employing actuator arrays under a flexible surface [ 15 ], by applying acoustic manipulation techniques [ 16 , 17 , 18 , 19 ], etc.…”