Dynamic Modeling of an Axially Moving Beam in Rotation: Simulation and Experiment

Abstract

In this paper, we consider a beam which has a rotational and translational motion. A time-varying partial differential equation and the boundary conditions are derived to describe the lateral deflection of the beam. For multivariable control, an approximated model is also derived by using the assumed mode method. The validity of the approximated model is investigated by the experiment. For different repositional motions, response of the beam is further investigated by computer simulation. Application of the beam to flexible robotic manipulators is discussed with simulation results.

Modeling of flexible-link manipulators with prismatic joints

“…In this paper, we present numerical simulations, with U 0:778 m/s and smallest U g = 59:34 m/s 4) Once the convective terms are dropped, we are left with the standard Euler-Bernoulli beam equation for a clamped-mass cantilever. Separation of variables or the assumed modes method can then be used with the eigen-frequencies based on the fully extended length l 0 : Even if the lengthis changing continuously with time (slowly compared to U g ) we can still assume that the "eigen-modes" can be used, i.e., the mode shape of the translating beam at every instant of time can be approximated by that of a cantilever beam [11]. However, we have to solve for the slowly and continuously changing "eigen-frequencies" (often called "quasi-frequencies" [18]) at each instant of time.…”

“…Wang and Wei [10] studied the vibration problem of a moving slender prismatic beam using a Galerkin approximation with time-dependent basis functions and by applying Newton's second law. Yuh and Young [11] presented the experimental results to validate the approximated dynamic model derived using assumed modes method for a flexible beam which has a rotational and translational motion. In all the aforementioned works, it is invariably assumed that the translating flexible links can be modeled as beams in flexure with clamped-free boundary conditions, leading to a time-independent frequency equation [7], [12], [14].…”

“…Modeling and control of manipulators with flexible links having only revolute joints have been discussed extensively in the literature [1]- [6], while the research on modeling prismatic jointed flexiblelink manipulators is limited [7]- [11]. When a link with the prismatic joint is modeled as flexible, the system becomes a moving boundary value problem.…”

Active Vibration Control of an Axially Translating Robot Arm with Rotating-Prismatic Joint Using Self-Sensing Actuator

“…The internal and external damping effects were also included in the model. Yuh and Young [10] analyzed the dynamics of a beam experiencing a combination of rotational and translational motions. An approximation scheme was developed by using assumed modes method.…”

Relative-Error-Based Finite Element Analysis of Axially Moving Beams

“…A modified Galerkin's method is used to solve the equation of motion of an axially moving beam [24]. The assumed-modes methods are used to compare the simulation results with those obtained experimentally [25]. Stylianou et al [26][27] developed elements with time-varying domains to investigate the dynamics and stability analysis of the flexible extendible beam under more general configurations by the finite element method.…”