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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…

One Domino

Domino

One Domino

"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.

Mark Twain saying "Sono Dispiacentissimo" to an Italian servant.

Mark Twain Speaking Italian

Mark Twain saying "Sono Dispiacentissimo" to an Italian servant.

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…

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 1

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 10

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 100

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 101

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 11

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 12

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 13

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 14

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 15

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 16

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 17

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 18

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 19

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 2

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 20

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 21

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 22

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 23

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 24

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 25

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 26

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 27

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 28

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 29

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 3

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 30

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 31

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 32

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 33

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 34

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 35

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 36

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 37

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 38

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 39

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 4

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 40

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 41

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 42

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 43

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 44

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 45

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 46

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 47

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 48

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 49

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 5

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 50

Geometric pattern for translation and rotation exercises.

Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 51

Geometric pattern for translation and rotation exercises.