Atwood's machine illustrates the effects of force in producing motion.

Atwood's Machine

Atwood's machine illustrates the effects of force in producing motion.

Biceps muscle attached to the radius.

Biceps Muscle and Radius

Biceps muscle attached to the radius.

"If the plane is inclined downwards, the ball is instantly thrown into motion, because the centre of gravity then falls forward of that motion, or the point on which the ball rests." -Comstock 1850

Center of Gravity of a Ball Rolling on an Incline

"If the plane is inclined downwards, the ball is instantly thrown into motion, because the centre of…

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…

"Attach a ball, for instance, to a cord; and , fastening the end of the cord at a point, O, give a quick impulse to the ball. It will be found to move in a circle, ABCD, because the cord keeps it within a certain distance of the centre (sic). Were it not for this, it would move in a straight line." —Quackenbos 1859

Centrifugal Force

"Attach a ball, for instance, to a cord; and , fastening the end of the cord at a point, O, give a quick…

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…

"Compound motion is that which is produced by two or more forces, acting in different directions, on the same body, at the same time." -Comstock 1850

Compound Motion

"Compound motion is that which is produced by two or more forces, acting in different directions, on…

"This is the curve of the heart cam for converting uniform rotary motion into uniform reciprocal motion." —French, 1911

Curve, Heart Cam

"This is the curve of the heart cam for converting uniform rotary motion into uniform reciprocal motion."…

"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…

"A drill to which a steady momentum is imparted by means of a fly-wheel having a reciprocating motion like that of the balance-wheel of a watch." -Whitney, 1911

Fly Drill

"A drill to which a steady momentum is imparted by means of a fly-wheel having a reciprocating motion…

"Thus, if we suppose the conducting wire be placed in a vertical situation, as shown, and p, n, the current of positive electricity to be descending through it, from p to n, and if throught the point c in the wire in the plane NN be taken, perpendicular to p, n, that is in the present case a horiczontal plane, then if any number of circles be described in that plane, having c for thier common centre, the action of the current on the wire on upon the north pole of the magnet, will be to move it in a direction corresponding to the motion of the hands of a watch, having the dial towards the positive pole of the battery." -Comstock 1850

Circular Motion of the [Electric] Fluid

"Thus, if we suppose the conducting wire be placed in a vertical situation, as shown, and p, n, the…

"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…

A piece in clocks and watches that converts rotational motion into oscillation, as in a pendulum.

Deadbeat Escapement

A piece in clocks and watches that converts rotational motion into oscillation, as in a pendulum.

A piece in clocks and watches that converts rotational motion into oscillation, as in a pendulum.

Recoiling Escapement

A piece in clocks and watches that converts rotational motion into oscillation, as in a pendulum.

"Friction-cones. a and b, cones; c, fork. In machinery, a form of friction-coupling consisting of two cones, one of which is fitted into the other and communicates its motion to it by means of the friction between the two surfaces." -Whitney, 1911

Friction Cones

"Friction-cones. a and b, cones; c, fork. In machinery, a form of friction-coupling consisting of two…

"Of all the contrivances for regulating the motion of machinery, this is said to be the most effectual. It will be readily understood by the following description. It consists of two heavy iron balls b, attached to the extremities of the two rods, b, e. These rods play on a joint at e, passing through a mortice in the vertical stem d, d. At f, these pieces are united, by joints to two short rods, f, h, which, at their upper ends, are again connected by joints at h, to a ring which slides upon the vertical stem d d." &mdash;Comstock, 1850

Governor

"Of all the contrivances for regulating the motion of machinery, this is said to be the most effectual.…

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.

"2 wheels revolving in contact, but in different planes, so as to transfer motion from one plane to another." &mdash; Williams, 1889

Mitre-wheels

"2 wheels revolving in contact, but in different planes, so as to transfer motion from one plane to…

The aggregate of the components of momentum.

Components of Momentum

The aggregate of the components of momentum.

"Device used to prove that all things fall at the same rate due to gravity. When the device is triggered, one object is dropped while anothe object is shot horizontally from within, with the result being that both objects strike the ground at the same time." &mdash;Hallock 1905

Projectile Motion

"Device used to prove that all things fall at the same rate due to gravity. When the device is triggered,…

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…

"Its mechanism may be understood by the means of the subjoined figure, B represents the end of the beam, which is pulled downward, and pushed upward, by the motion of the piston-rod R P; the motion of B is in the direction of the dotted curve; that of R P is rectilinear." &mdash;Comstock, 1850

Parallel Motion

"Its mechanism may be understood by the means of the subjoined figure, B represents the end of the beam,…

"When the pendulum is drawn from its vertical position, the force of gravity, MG, is resolved into two components, one of which, MC, produces pressure at the point of support, while the other, MH, acts at right angles to it, producing motion toward N." -Avery 1895

Motion of a Pendulum

"When the pendulum is drawn from its vertical position, the force of gravity, MG, is resolved into two…

"The motion of Saturn, Jupiter, and Mars with respect to Earth." &mdash; Encyclopedia Britanica, 1893

Planet Rotations

"The motion of Saturn, Jupiter, and Mars with respect to Earth." — Encyclopedia Britanica, 1893

"Suppose a cannon be loaded with a ball, and placed on top of a tower, at such a height from the ground, that it would take just three seconds for the ball to descend from it to the ground, if let fall perpendicularly. Now, suppose the cannon to be fired in an exact horizontal direction, and at the same instant, the ball to be dropped towards the ground. They will both reach the ground at the same instant..." -Comstock 1850

Projectile Motion of a Cannonball

"Suppose a cannon be loaded with a ball, and placed on top of a tower, at such a height from the ground,…

"[This illustration] shows the path of a stone thrown obliquely from the hand. The propelling force sends it in a straight line to A, and would take it on in the same direction to B, were it not that, as soon as its velocity becomes sufficiently diminished, gravity and the air's resistance give it a circular motion to C, and finally bring it to the earth at D." &mdash;Quackenbos 1859

Projectile Motion of a Stone

"[This illustration] shows the path of a stone thrown obliquely from the hand. The propelling force…

"Thus, we have a cannon planted on a towwer at such a height that it would take four seconds for a ball to fall from it to the ground. Dropped from the cannon's mouth, in the first second a ball would reach A; in the next, B; in the third, C; and in the fourth D." &mdash;Quackenbos 1859

Projectile Motion of a Cannon Ball

"Thus, we have a cannon planted on a towwer at such a height that it would take four seconds for a ball…

"Suppose a, b, to be a marble floor, and c, to be an ivory ball, which has be thrown towards the floor in the direction of the line c e; it will rebound in the direction of the line e d, thus making the two angles f and g exactly equal." -Comstock 1850

Reflected Motion

"Suppose a, b, to be a marble floor, and c, to be an ivory ball, which has be thrown towards the floor…

"If the ball approaches the floor under a larger or smaller angle, its rebound will observe the same rule [of reflected motion]." -Comstock 1850

Reflected Motion

"If the ball approaches the floor under a larger or smaller angle, its rebound will observe the same…

"... if a ball be thrown from F against the surface B C so as to strike it perpendicularly at A, it will return in the line A F. If thrown from D however, it will glance off on the other side of the perpendicular, at the same angle, to E." &mdash;Quackenbos 1859

Reflected Motion

"... if a ball be thrown from F against the surface B C so as to strike it perpendicularly at A, it…

"The ball C is placed on a square frame between two upright wires, on each of which a ball slides so as to strike C when it descends. Let the ball A drop, and it will drive C to D... Let the ball B drop, and it will drive C to E; this is simple motion. Let A and B drop at the same instant, and they will drive C to F; this is resultant motion." &mdash;Quackenbos 1859

Resultant Motion with Ball

"The ball C is placed on a square frame between two upright wires, on each of which a ball slides so…

"We have an example of resultant motion in a boat which a person attempts to row north across a river, while the tide carries it to the east. Each force produces the same effect as if acted alone; and the boatman, when he has crossed the river, will find himself neither due north nor due east of the point from which he started, but northeast of it." &mdash;Quackenbos 1859

Resultant Motion with Boat

"We have an example of resultant motion in a boat which a person attempts to row north across a river,…

"Let, for instance, the force used by the boatman be twice as great as that of the tide. Then by the time he would reach B, the tide would have carried his boat one-half of that distance, to D." &mdash;Quackenbos 1859

Resultant Motion with Boat

"Let, for instance, the force used by the boatman be twice as great as that of the tide. Then by the…

"Fleming's rule for direction of induced current. Extend the thumb, forefinger and middle finger of the right hand [as shown]. Place the hand [so that] the thumb will point in the direction in which the conductor moves, the forefinger in the direction of the lines of force (N to S), then will the middle finger point in the direction in which the induced current flows." -Hawkins, 1917

Right Hand Rule of Induced Current

"Fleming's rule for direction of induced current. Extend the thumb, forefinger and middle finger of…

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.

Water-belt for transmitting motion, from 1875.

Water-Belt

Water-belt for transmitting motion, from 1875.