A Novel Dynamic Model for Single Degree-of-Freedom Planar Mechanisms Based on Instant Centers

2015 ◽  
Vol 8 (1) ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Dynamic Model ◽  
Virtual Work ◽  
Degree Of Freedom ◽  
Dynamic Problems ◽  
Planar Mechanisms ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Proposed Model ◽  
External Forces

Many even complex machines employ single degree-of-freedom (single-dof) planar mechanisms. The instantaneous kinematics of planar mechanisms can be fully understood by analyzing where the instant centers (ICs) of the relative motions among mechanism’s links are located. ICs' positions depend only on the mechanism configuration in single-dof planar mechanisms and a number of algorithms that compute their location have been proposed in the literature. Once ICs positions are known, they can be exploited, for instance, to determine the velocity coefficients (VCs) of the mechanism and the virtual work of the external forces applied to mechanism's links. Here, these and other ICs' properties are used to build a novel dynamic model and an algorithm that solves the dynamic problems of single-dof planar mechanisms. Then, the proposed model and algorithm are applied to a case study.

Systematic Use of Instant Centers in the Dynamics Analysis of Single-DOF Planar Mechanisms

2015 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Dynamic Model ◽  
Virtual Work ◽  
Dynamics Analysis ◽  
Dynamic Problems ◽  
Planar Mechanisms ◽  
Proposed Model ◽  
External Forces ◽  
Relative Motions

Many even complex machines employ single-dof planar mechanisms. The instantaneous kinematics of planar mechanisms can be fully understood by analyzing where the instant centers (ICs) of the relative motions among mechanism’s links are located. ICs’ positions depend only on the mechanism configuration in single-dof planar mechanisms and a number of algorithms that compute their location have been proposed in the literature. Once ICs positions are known, they can be exploited, for instance, to determine the velocity coefficients of the mechanism and the virtual work of the external forces applied to mechanism’s links. Here, these and other ICs’ properties are used to build a novel dynamic model and an algorithm that solves the dynamic problems of single-dof planar mechanisms. Then, the proposed model and algorithm are applied to a case study.

Ground Motion Prediction Model for the Peak Inelastic Displacement of Single-Degree-of-Freedom Bilinear Systems

2018 ◽  
Vol 34 (3) ◽  
pp. 1177-1199 ◽  
Author(s):  
Pablo Heresi ◽  
Héctor Dávalos ◽  
Eduardo Miranda
Keyword(s):  
Prediction Model ◽  
Ground Motion ◽  
Degree Of Freedom ◽  
Motion Prediction ◽  
Ground Motion Prediction ◽  
Vibration Period ◽  
Single Degree Of Freedom ◽  
Inelastic Displacement ◽  
Single Degree ◽  
Proposed Model

This paper presents a ground motion prediction model (GMPM) for estimating medians and standard deviations of the random horizontal component of the peak inelastic displacement of 5% damped single-degree-of-freedom (SDOF) systems, with bilinear hysteretic behavior and 3% postelastic stiffness ratio, directly as a function of the earthquake magnitude and the distance to the source. The equations were developed using a mixed effects model, with 1,662 recorded ground motions from 63 seismic events. In the proposed model, the median is computed as a function of the vibration period and the normalized strength of the system, as well as the event magnitude and the Joyner-Boore distance to the source. The standard deviation of the model is computed as a function of the vibration period and the normalized strength of the system. The proposed model has the advantage of not requiring an auxiliary elastic GMPM to predict the median and dispersion of peak inelastic displacement.

Kinetostatic Synthesis of Coupled Serial Chains

1998 ◽  
Author(s):  
Venkat Krovi ◽  
G. K. Ananthasuresh ◽  
Vijay Kumar
Keyword(s):  
Virtual Work ◽  
Degree Of Freedom ◽  
Optimal Synthesis ◽  
Synthesis Problem ◽  
Equilibrium Equations ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Angular Velocities ◽  
Kinematic Loop ◽  
Serial Chains

Abstract Single Degree-of-freedom Coupled Serial Chain (SDCSC) mechanisms are a novel class of modular and compact mechanisms with single degree-of-freedom actuation and control. In this paper, the kinetostatic synthesis of SDCSC mechanisms is addressed. Using the principle of virtual work, the static force equilibrium equations are developed for two-link SDCSCs. These are combined with the previously developed kinematic loop-closure equations to solve the kinetostatic precision point synthesis problem. Since the ratios of the angular velocities at the joints are constants by virtue of cable-pulley coupling in SDCSCs, it possible to render the kinetostatic equations linear in terms of the mechanism parameters. As a result, the solution of the precision point synthesis problem of SDCSCs becomes simpler compared to that of the four-bar mechanism. In order to meet additional criteria such as minimizing the maximum torque required over the entire range of motion of the mechanism, an optimization problem is formulated. The free choices in the precision point synthesis are used as variables in the optimal synthesis problem. The paper also addresses how torsional springs at the joints can be utilized to reduce the required input torque in supporting a specified load at the end-effector. Numerical examples are presented to illustrate the precision point and the optimal synthesis of two-link SDCSC mechanism with and without torsional springs at the joints.

Design of Multi-Degree-of-Freedom Planar Morphing Mechanisms With Single-Degree-of-Freedom Sub-Chains

2015 ◽  
Author(s):  
Lawrence Funke ◽  
James P. Schmiedeler
Keyword(s):  
Optimization Techniques ◽  
Degree Of Freedom ◽  
Multiple Forms ◽  
Polymer Extrusion ◽  
Planar Mechanisms ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Highly Nonlinear ◽  
Morphing Wings ◽  
Gradient Based

This paper deals with the synthesis of multi-degree-of-freedom planar mechanisms by breaking the problem into the synthesis of multiple single-degree-of-freedom planar mechanisms. Specifically, this paper investigates synthesizing shape-changing mechanisms capable of matching multiple closed profiles with significant changes in shape. These mechanisms can be used for applications such as morphing wings or morphing dies for polymer extrusion. Well established synthesis techniques for single-degree-of-freedom planar mechanisms are used and reviewed for completeness. The paper then compares multiple forms of two optimization techniques used to find suitable mechanisms. The problems investigated herein are highly nonlinear and highly constrained; therefore, advanced optimization strategies are needed. This paper uses both gradient-based optimization and a genetic algorithm (GA) to find mechanisms capable of matching the design profiles. It also looks at additions to the GA that leverage the presence of the single-degree-of-freedom subchains. The gradient-based optimization and GA with additions were able to find mechanisms with better matching error than the blind GA. However, the improvement was modest and not always present, indicating that it is likely best to start with the blind GA and introduce gradient-based optimization, additions to the GA, and changes in the setting as needed to improve results.

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