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In this Chapter, new methods for the full shaking force and shaking moment balancing of linkages are considered. In Sect. 4.1, a new solution for the full shaking force and shaking moment balancing of four-bar linkages is discussed, which allows the complete shaking force and shaking moment balancing of in-line four-bar linkages with constant input speed by adding a class-two Assur group, i.e. a group which does not add any supplementary degree of freedom into the mechanism. It should be noted that the balancing of the shaking moment without counter-rotations of three particular classes of four-bar linkages is known and it was mentioned in the overview (see Sect. 2.1). However, such a method cannot be extended to general four-bar linkages. In the mentioned Section, it is proposed to dynamically balance the in-line four-bar linkages by adding articulated dyads.
The object of the approach presented in Sect. 4.2 is to provide the conditions for a complete shaking force and shaking moment balancing of linkages with a relatively small increase of the total mass of movable links by mounting the gear inertia counterweights on the base of the mechanism. The method involves connecting to the mechanism to be balanced a two-link group forming a pantograph with the crank and coupler. Three versions of sub-linkages are considered: (1) the articulation dyad; (2) the asymmetric link with three rotational pairs; (3) the crank-slider mechanism. The method is illustrated by new balancing schemes for the Stephenson and Watt linkages. An advantage of the schemes outlined here is the fact that all the gear inertia counterweights needed for balancing the shaking moment are mounted on the mechanism frame, which is constructively more efficient.
The complete shaking force and shaking moment balancing of spatial linkages is very complicated and the majority of the works have been concentrated on complete shaking force balancing or partial shaking force and shaking moment balancing. The solution proposed in the Sect. 4.3 shows that it is possible to achieve a complete shaking force and shaking moment balancing of the RSS’R spatial linkage by using a coupler with a special shape. In such an approach, the mass of the connecting coupler is substituted dynamically by concentrated masses located at joints. This allows for the transformation of the problem of linkage dynamic balancing into a problem of balancing rotating links carrying concentrated masses.
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A “physical pendulum” is a link which has such a distribution of masses that it allows the dynamic substitution of link’s mass and inertia by two concentrated masses.
After the static substitution of the masses of the link by point masses, it is necessary to take into account the change of the moment of inertia of the link.
The parameters of link 5 are selected so that the com of link 4, with the point masses m C and m D taken into account, coincides with the working point G of the pantograph, due to which the motion of this link is represented as a translational rectilinear motion of its com and a rotary motion relative to point G.
The expressions concerning the determination of masses and mass moments of inertia have been taken from (Favorin 1970).
- Complete Shaking Force and Shaking Moment Balancing of Linkages
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