Dynamics and Control of a Translating Flexible Beam With a Prismatic Joint

Abstract

The complete dynamic model of a translating flexible beam, with a tip mass at one end and emerging from or retracting into a rigid base at the other, is presented. The model considers the effect of elastic and translational motions of the beam on each other. The properties of the eigenfunctions of a fixed-free beam are exploited to obtain closed-form expressions for several domain integrals that arise in the model. It is shown that neglecting the effect of elastic motion on the rigid body motion leads to inaccuracies in positioning control. Issues associated with the feedback control of such a beam are discussed.

Dynamic analysis of an axially translating viscoelastic beam with an arbitrarily varying length

“…This is due to the fact that the flexural rigidity of the beam is reduced during the extension mode and enhanced during the retraction mode; i.e., the beam becomes somewhat "softer" and "stiffer", respectively, during the extrusion and retraction operations (cf. [17]). …”

“…Base on the finite element method, Stylianou and Tabarrok [15,16] investigated the axially moving slender beam; their numerical results specified that the beam would be stabilized in extension and unstabilized in retraction. The dynamics and control of a translating flexible beam with a tip mass at one end emerging from or retracting into a rigid base was proposed by Tadikonda and Baruh [17]; they exploited the eigenfunctions of a cantilever beam to obtain closed-form expressions for several domain integrals that arise in the model, which showed that the coupling effect of elastic and translational motions is very important to the beam control. Moreover, using Hamiltonian dynamic analysis, Wang et al [18] investigated an axially translating elastic Bernoulli-Euler cantilever beam featuring time-variant velocity.…”

Boundary Control of an Axially Moving Steel Strip under a Spatiotemporally Varying Tension

“…Especially, the dynamics analysis and control for axially moving beams have received a growing attention due to the entrance of new applications in flexible robotic manipulators and flexible space structures (5) - (9) . Particularly, vibration control schemes on axially moving strings include Yang et al (10) , Chung and Tan (11) , Lee and Mote (12) , Fung et al (13) , and Li et al (14) , and those on axially moving beams include Choi et al (15) , Hong et al (16) , Lee and Mote (17) , Li and Rahn (18) , and Fung et al (19) The boundary force control has several advantages over control schemes acting within the spatial domain (e.g., distributed force control).…”

Modeling of flexible-link manipulators with prismatic joints

“…When a link with the prismatic joint is modeled as flexible, the system becomes a moving boundary value problem. Moving boundary value problems have been considered in other context such as axially moving beam problems [12]- [14], and deployment dynamics of flexible spacecraft [15], [16].…”

“…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]. The "free" boundary condition however may lead to inaccurate mode shapes and over-estimated eigen frequencies which may have destabilizing effect when the translating flexible robot link carries a payloador when a wrist is attached at distal end of the axially moving elastic beam [19].…”