ClipArt ETC
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…

Illustration used to compare the surfaces of a cylinder and a sphere.

Comparative Surfaces Of A Cylinder And Sphere

Illustration used to compare the surfaces of a cylinder and a sphere.

Illustration of a cylinder showing, "If a piece of paper is fitted to cover the convex surface of a prism or a cylinder, and then unrolled, its form will be that of a rectangle, as ABCD."

Surfaces Of A Cylinder

Illustration of a cylinder showing, "If a piece of paper is fitted to cover the convex surface of a…

"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 of an irregular surface abdc projected upon the flat surface ABCD.

Projection Of An Irregular Surface

Illustration of an irregular surface abdc projected upon the flat surface ABCD.

"A lens is a transparent body the two refracting surfaces of which are curved, or one of which is curved and the other plane.(1) Double convex(2) Plano convex(3) Meniscus(4)Double concave(5) Plano concave(6) Concavo concave." -Avery 1895

Lens

"A lens is a transparent body the two refracting surfaces of which are curved, or one of which is curved…

"The shape of the double convex lens, d, c, is that of two plano-convex lenses, placed with their plane surfaces in contact, and consequently the focal distance of this lens is nearly the centre of the sphere of which one of its surfaces is a part." -Comstock 1850

Double Convex Lens

"The shape of the double convex lens, d, c, is that of two plano-convex lenses, placed with their plane…

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…

Illustration of a pentagonal prism showing, "If a piece of paper is fitted to cover the convex surface of a prism or a cylinder, and then unrolled, its form will be that of a rectangle, as ABCD."

Surfaces Of A Prism

Illustration of a pentagonal prism showing, "If a piece of paper is fitted to cover the convex surface…

Illustration showing a section of the rolling surfaces by a plane perpendicular to their straight line of contact.

Section of Rolling Surfaces

Illustration showing a section of the rolling surfaces by a plane perpendicular to their straight line…

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.