Kinematics of Machines; An Elementary Text-Book

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1903 Excerpt: ... BB a length DCt equal to the length of DC measured along A A. Draw B,CD1, representing the centrode B in the position it occupies when a is the point of contact of the two bodies and C is their virtual centre, and make CDl = CD. Join aDv Then since the outline of bb' may be regarded as attached to the centrode B, any point on that outline having the same position in relation to C1 and D that the point a has in relation to C and D1 will be the point that touches a when the centrodes touch at C. Accordingly we need only make bD = aDl and bCt=aC in order to determine the position of b. The point b is then a point on the required profile which will touch the point a when C is the virtual centre of the two bodies. In the same way we can determine any other point on the profile required, and it only remains to provide the resulting body with the restraint required to prevent any other motion than that desired. This would in general be done by so forming the body bb' that it possesses at any instant three points of contact with aa', the normals to these points always intersecting at the virtual centre. It would, in fact, be necessary to repeat the construction of Fig. 122, assuming two other portions of the outline of aa', and finding two new portions of the outline of bb', the centrodes, of course, remaining the same as before. It may be noted that while the relative motion of the centrodes is one of simple rolling, that of the two outlines is in general rolling and sliding combined. 63. Condition for Uniform Velocity Ratio.--We have seen in § 60 that when two bodies are in continuous contact and are capable of constrained relative motion, the normals at the points of contact must intersect at the virtual centre. Consider now the case of three bodies (Fig. ...