Research Papers

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

[+] Author and Article Information
Raffaele Di Gregorio

Department of Engineering,
University of Ferrara,
Via Saragat, 1,
Ferrara 44122, Italy
e-mail: raffaele.digregorio@unife.it

1Corresponding author.

Manuscript received January 9, 2015; final manuscript received June 19, 2015; published online August 18, 2015. Assoc. Editor: Andreas Mueller.

J. Mechanisms Robotics 8(1), 011013 (Aug 18, 2015) (8 pages) Paper No: JMR-15-1006; doi: 10.1115/1.4030986 History: Received January 09, 2015

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.

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Grahic Jump Location
Fig. 1

Intersection of two lines, the IC Iij lies on: (a) the two lines are identified through the A–K theorem and (b) the two lines refer to either a slipping contact or a prismatic pair [13]

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Fig. 2

Instantaneous relative motion between links j and i: (a) instantaneous rotation (Iji is a finite point of the motion plane; the motion is uniquely defined by Iji and θ·ji) and (b) instantaneous translation (Iji is the point at infinity of the lines perpendicular to the translation direction; the motion is uniquely defined by the translation velocity s·jitji)

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Fig. 3

Generic scheme of a single-dof planar mechanism with m links (Gj, μj, and λj, for j = 2,…, m, are the center of mass, the mass, and the inertia moment about its center of mass, respectively, of the jth link)

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Fig. 4

Link j loaded by the resultant torque, Mjk, about Gj and the resultant force, Rjfj, of all the active forces applied to it: (a) the link performs an instantaneous rotation about Ij1 and (b) the link performs an instantaneous translation parallel to tj1

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Fig. 5

VCs as a function of θ21 (a1 = 0.2 m, a2 = 0.1 m, a4 = 0.4 m, a5 = 0.2 m, and a6 = 0.2 m): (a) ν3 and ν5 and (b) ν6

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Fig. 6

The generalized inertia coefficient, J, (a) and its derivative with respect to θ21 (b) of the shaper mechanism with the geometry of Fig. 5 and the mass distribution data of Table 1 as a function of θ21

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Fig. 7

Generalized inertia torque, τ, as a function of θ21 in the case θ·21 = 20 rpm, θ··21 = 0, and a cutting force of 500 N

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Fig. 8

Link j: determination of Gj's position after the link pose, with respect to the frame, has been computed

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Fig. 9

Shaper mechanism: kinematic scheme and notations




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