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Illustration showing the periodic center of motion as it often happens when two positions of a line are known and they are moving in the same plane and we wish to find an axis about which this line could revolve to occupy the two given positions.

Periodic Center of Motion

Illustration showing the periodic center of motion as it often happens when two positions of a line…

Illustration showing a centroid, "the curve passing through the successive positions of the instantaneous centre of a body having a combined motion of rotation and translation is called a centroid." A smooth curve passes through the successive positions of the instantaneous centers (all the centers marked o)will be the centroid ab.

Centroid

Illustration showing a centroid, "the curve passing through the successive positions of the instantaneous…

"Since these curves are not closed, one pair cannot be used for continuous motion; but a pair of such curves may be well adapted to sectional wheels requiring a varying angular velocity." This figure shows an example of the process.

Motion of Open Curves

"Since these curves are not closed, one pair cannot be used for continuous motion; but a pair of such…

"If two equal ellipses, each turning about one of its foci, are placed in contact in such a way that the distance between the axes O<SUB>1</SUB> and O<SUB>2</SUB> is equal to the major axis of the ellipses, we shall find that they will be in contact on the line of centres and that the rolling arcs are of equal length."

Rolling of Equal Ellipses

"If two equal ellipses, each turning about one of its foci, are placed in contact in such a way that…

Illustration of the rolling of equal hyperbolas. If two equal hyperbolas are placed so that the distances between their foci O<SUB>1</SUB> and O<SUB>2</SUB>, and d and e, are each equal to fg=hk, they will make contact at some point c.

Rolling of Equal Hyperbolas

Illustration of the rolling of equal hyperbolas. If two equal hyperbolas are placed so that the distances…

Illustration of the rolling of equal parabolas. "The two parabolas may be considered as two ellipses with one focus of each removed to infinity."

Rolling of Equal Parabolas

Illustration of the rolling of equal parabolas. "The two parabolas may be considered as two ellipses…

Illustration showing how a rolling logarithmic spiral can be constructed by taking successive values of theta, starting from oc. The values of r can be calculated and then the curve can be plotted.

Construction of Logarithmic Spiral

Illustration showing how a rolling logarithmic spiral can be constructed by taking successive values…

Illustration showing the rolling of two logarithmic spirals of equal obliquity.

Rolling of Logarithmic Spirals

Illustration showing the rolling of two logarithmic spirals of equal obliquity.

Illustration showing that the rolling of non-cylindrical surfaces. "If the angular velocity ratio of two rolling bodies is not a constant, the pitch lines take, the conditions of pure rolling contact should be fulfilled, namely, the point of contact must be on the line of centres, and the rolling arcs must be of equal length.

Rolling of Non-cylindrical Surfaces

Illustration showing that the rolling of non-cylindrical surfaces. "If the angular velocity ratio of…

In this illustration, "the driven surface of the slide coincides with the tangent to the spiral, the line of centres being from o through c to infinity and perpendicular to the direction of motion of the slide.""

Logarithmic Spiral Sector

In this illustration, "the driven surface of the slide coincides with the tangent to the spiral, the…

Illustration showing the motion of translation of two parallel motions.

Motion of Translation

Illustration showing the motion of translation of two parallel motions.