Page:The Kinematics of Machinery.djvu/80

 when known for every instant, is called the relative motion of the point or if instead of a point we have a body, the relative motion of the body, to the portion of space surrounding us. If this were itself motionless, the absolute and relative motions of the point would be identical, but if not, they must differ. Absolute motion in the universe being of no importance in our investi- gations, we may limit the meaning of the term absolute motion, and understand by it only motion relative to the portion of space in which our observations are made, to the earth, for instance, or to a ship or a train.

We shall examine first the case in which this portion of space is a plane merely, the motions to be considered being thus motions in a plane.

Prop. I. The motion of a point P relatively to another point Q in the plane P Q takes place along the line P Q which joins those

P Q

. 13.

points, no matter what motion the point may have relatively to the plane itself. The motion of P relatively to Q and of Q to P is known when the distance P Q is known for every instant. This first proposition is not limited to motion in a plane, but is entirely applicable to the general motion of two points in space.

Example. The motion of the centre (P) of a planet relatively to that (Q) of a body around which it revolves in any orbit, is an oscillation along the line P Q joining their centres.

Prop. II. The motion of a point P relatively to a plane in which it moves* is known if its motion relatively to two fixed points A and B in the plane of motion be given.

The path of motion is then the locus of the vertex P of the triangle APE, which takes, for instance, the position A F B (Fig. 14).

Example. The motion of any point P in an ordinary connecting- rod relatively to the plane in which it swings, is a curve which can be


 * In Fig. 14 the plane of the paper.