Considering Link Flexibility in the Dynamic Synthesis of Closed-Loop Mechanisms: A General Approach

This paper has focused on the dynamic analysis of mechanisms with closed-loop configuration while considering the flexibility of links. In order to present a general formulation for such a closed-loop mechanism, it is allowed to have any arbitrary number of flexible links in its chain-like structure. The truncated assumed modal expansion technique has been used here to model link flexibility. Moreover, due to the closed nature of the mentioned mechanism, which imposes finite holonomic constraints on the system, the appearance of Lagrange multipliers in the dynamic motion equations obtained by Lagrangian formulation is unavoidable. So, the Gibbs-Appell (G-A) formulation has been applied to get rid of these Lagrange multipliers and to ease the extraction of governing motion equations. In addition to the finite constraints, the impulsive constraints, which originate from the collision of system joints with the ground, have also been formulated here using the Newton's kinematic impact law. Finally, to stress the generality of the proposed formulation in deriving and solving the motion equations of complex closed-loop mechanisms in both the impact and non-impact conditions, the computer simulation results for a mechanism with four flexible links and closed-loop configuration have been presented.

Analysis of Influence of a Crane Flexible Supports, Link Flexibility, and Joint Friction on Vibration Associated with Programmed Motion Execution

Background The paper presents vibration analysis of dynamic models of systems with flexible mechanical components, friction modeled and subjected to position and kinematic programmed constraints, which can be imposed as control goals, work or service task demands. Methods The constrained dynamics is derived using an automated computational procedure dedicated to constrained systems. The procedure was successfully implemented to rigid system models. A class of systems composed of flexible parts and subjected to programmed motions is considered in the paper. Their motion analysis has to be accompanied by vibration inspection. The novelty of the presented approach is in the possibility of analyzing system motions and vibrations that can be induced by the presence of programmed constraints. Conclusions The constrained motion is examined by the example of a crane model equipped with a flexible link, e.g. a jib, friction modeled in its joints and subjected to programmed constraints. The example delivers a realistic work situation, in which the crane carries loads and moves according to the programmed constraint put on motion.

Nonlinear dynamics and control of crank–slider mechanism with link flexibility and joint clearance

Dynamical behaviors and control of planar crank–slider mechanism considering the effects of joint clearance and link flexibility are studied. A control scheme for maintaining continuous contact is proposed. It was observed that using one actuator for control scheme might cause the actuator to reach its saturation limit, a problem that was bypassed by installing an additional actuator on connecting rod. In one actuator case, only continuous contact can be obtained, while with the aid of two actuators, point contact can be achieved. Great improvements in the performance of mechanism and reduction of vibrations are observed in the case of using an additional actuator.