MECHANICS. 



61 



Another contrivance for the same 

 purpose is exhibited in fig. 111. A B is 

 a lever working on the centre C. B D 

 is jointed at B to the extremity of this 

 lever, and at D to a beam a b, which 

 moves in guides m n. It is evident that 

 a reciprocating circular motion at A will 

 produce a reciprocating rectilinear mo- 

 tion in the beam a b, and vice versa. 



(112.) To convert a continued circu- 

 lar motion into another continued cir- 

 cular motion. 



In a motion of continued rotation, two 

 things are to be considered; the axis 

 round which the rotation is made, and 

 the velocity, or the number of revolu- 

 tions performed in a given time. 



If, by a rotation round one axis, it be 

 required to produce a rotation round 

 another axis parallel to it, the problem 

 may be solved thus : place two wheels 

 on the two axes, so that they shall be in 

 the same plane at right angles to the 

 given axes. Let these wheels act one 

 upon the other either by the friction of 

 their edges or by a strap, or chain, or, 

 finally, by teeth. If they act either by 

 friction or by teeth, the rotation round 

 the two axes will be made in contrary 

 directions ; but if they act by a strap or 

 chain, the rotation will be in the same 

 direction if the strap be crossed ; but 

 otherwise in opposite directions. 



The rotation may be produced in the 

 same direction when the wheels act by 

 teeth, or friction, by interposing a third 

 wheel between those which are placed 

 upon the given axes. There is an ad- 

 vantage in the use of a strap, in cases 

 where the two axes are at a consider- 

 able distance one from the other ; as it 

 does not render the multiplication of 

 wheels necessary. 



In cases where the resistance is too 

 great for the use of a strap, rotation 

 may be transmitted to a number of pa- 

 rallel shafts by means of bevelled 

 wheels on a shaft at right angles to 

 them. This method of giving rotation 

 to several parallel shafts is represented 

 in fig. 112. 



Fig. 112. 



which it is received, the wheels by 

 which it is transmitted, whether by 

 friction, straps, or teeth, are to be of 

 equal diameters ; and in whatever pro- 

 portion the velocity is to be increased 

 or diminished, the diameter of the wheel 

 must be diminished or in creased exactly 

 in the same proportion. 



We have here supposed that the 

 shafts through which the rotation is 

 transmitted are parallel. Suppose they 

 are not parallel, but their directions in- 

 tersect ; the rotation may then be trans- 

 mitted by bevelled wheels placed upon 

 the shafts, as represented infig.47 (70.) ; 

 and if the velocity of rota ion be re- 

 quired to be changed, the cones, from 

 which the bevelled wheels are formed, 

 must have different angles, as explained 

 in (70.) 



If the shafts be at a considerable dis- 

 tance one from the other, the bevelled 

 wheels placed upon them cannot con- 

 veniently act one upon the other imme- 

 diately. In this case a third shaft must 

 be used, bearing two bevelled wheels, as 

 represented in fig. 113, through which 

 the motion is transmitted. 



Fig. 113. 



When the velocity of rotation is to be 

 the same as that of the shaft from 



This method of connecting the shafts 

 by a third shaft will also serve when the 

 two given shafts are not in the same 

 plane. 



\\ hen the shafts, between which the 

 motion is to be transmitted, are at 

 right angles, two bevelled wheels, such 

 as are represented in fig. 47, are most 

 frequently used. A crown and spur 

 wheel would, however, serve the same 

 purpose, and are sometimes resorted 

 to. This arrangement is represented in 

 fig- H4. 



Rotation round an axis miy be trans- 

 ferred to an axis at right angles to it by 

 means of a perpetual screw working in 

 a toothed wheel, as represented in fig. 

 86. In this figure the axis of the wheel 

 is represented parallel to the horizon ; 

 but it is plain that the same effect will 



