Introduction to Mechanisms
Mechanism: the fundamental physical or chemical processes
involved in or responsible for an action, reaction or other natural
Machine: an assemblage of parts that transmit forces, motion
and energy in a predetermined manner.
Simple Machine: any of various elementary mechanisms having
the elements of which all machines are composed. Included in
this category are the lever, wheel and axle, pulley, inclined plane,
wedge and the screw.
The word mechanism has many meanings. In kinematics, a mechanism is a means of
transmitting, controlling, or constraining relative movement (Hunt 78). Movements which are
electrically, magnetically, pneumatically operated are excluded from
the concept of mechanism. The central theme for mechanisms is rigid
bodies connected together by joints.
A machine is a combination of rigid or resistant bodies,
formed and connected so that they move with definite relative motions
and transmit force from the source of power to the resistance to be
overcome. A machine has two functions: transmitting definite relative
motion and transmitting force. These functions require strength
and rigidity to transmit the forces.
The term mechanism is applied to the combination of
geometrical bodies which constitute a machine or part of a machine. A
mechanism may therefore be defined as a combination of
rigid or resistant bodies, formed and connected so that they move with
definite relative motions with respect to one another (Ham et al. 58).
Although a truly rigid body does not exist, many engineering
components are rigid because their deformations and distortions are
negligible in comparison with their relative movements.
The similarity between machines and mechanisms is
- they are both combinations of rigid bodies
- the relative motion among the rigid bodies are definite.
The difference between machine and mechanism is
that machines transform energy to do work, while mechanisms so not
necessarily perform this function. The term machinery
generally means machines and mechanisms. Figure 2-1
shows a picture of the main part of a diesel engine. The
mechanism of its cylinder-link-crank parts is a slider-crank
mechanism, as shown in Figure 2-2.
Figure 2-1 Cross section of a power
cylinder in a diesel engine
Figure 2-2 Skeleton outline
Figure 2-3a shows an inclined
plane, AB is the base, BC is the height and AC the inclined
plane. With the use of the inclined plane a given resistance can
be overcome with a smaller force than if the plane is not used. For
example, in Figure 2-3b, suppose we wish to raise
a weight of 1000 lb. through the vertical distance BC = 2 ft. If this
weight were raised vertically and without the use of the inclined
plane the force 1000 lb. would have to be exerted through the distance
BC. If, however, the inclined plane is used and the weight is moved
over its inclined plane AC, a force of only 2/3 of 1000 lb. or 667
lb. is necessary, although this force is exerted through a distance AC
which is greater than distance BC.
Figure 2-3 Inclined plane
Using an inclined plane requires a smaller force exerted
through a greater distance to do a certain amount of work.
Letting F represent the force required to raise a given weight on
the inclined plane, and W the weight to be raised, we have the proportion:
One of the most common application of the principle of the inclined plane is in the screw
jack which is used to overcome a heavy pressure or raise a
heavy weight of W by a much smaller force F applied at
the handle. R represents the length of the handle and P
the pitch of the screw, or the distance advances in one
Figure 2-4 The screw jack
Neglecting the friction the following rule is used: The force F
multiplied by the distance through which it moves in one complete turn
is equal to the weight lifted times the distance through which it is
lifted in the same time. In one complete turn the end of the handle
describes a circle of circumference 2R. This is the
distance through which the force F is exerted.
Therefore from the rule above
Suppose R equals 18 in., P equals 1/8 in. and the weight
to be lifted equals 100,000 lb., then the force required at F
is then 110 lb. This means that, neglecting friction, 110 lb. at
F will raise 100,000 lb. at W, but the weight lifted
moves much slower than the force applied at F.
A gear, or toothed wheel, when in operation, may actually be
considered as a lever with the additional feature that it can be rotated
continuously, instead of rocking back and forth through a short
distance. One of the basic relationships for a gear is the number
of teeth, the diameter, and the rotary velocity of gears. Figure 2-5 shows the ends of two shafts A and B
connected by 2 gears of 24 and 48 teeth respectively. Notice that the
larger gear will make only one-half turn while the smaller makes a
complete turn. That is, the ratio of speeds (velocity ratio) of the
large to the smaller is as 1 to 2.
Figure 2-5 Gears
The gear that is closer to the source of power is called the
driver, and the gear that receives power from the driver is
called the driven gear.
A gear train may have several drivers and several driven gears.
Figure 2-6 Gear train
When gear A turns once clockwise, gear B turns 4 times
counter-clockwise and gear C turns once clockwise. Hence gear B does
not change the speed of C from what it would have been if geared
directly to gear A, but it changes its direction from counterclockwise
The velocity ratio of the first and last gears in a train of simple gears
dose not changed by putting any number of gears between them.
Figure 2-7 shows compound gears in which
two gears are on the middle shaft. Gears B and D rotate at the same
speed since they are keyed (fixed) to the same shaft. The number of
teeth on each gear is given in the figure. Given these numbers, if
gear A rotates at 100 r.p.m. clockwise, gear B turns 400
r.p.m. (rotations per minute) counterclockwise and gear C turns 1200
Figure 2-7 Compound gears
It is important when working with gears to know what number of teeth
the gears should have so that they can mesh properly in a gear train.
The size of the teeth for connecting gears must be match properly.
Belts and pulleys are an important part of
most machines. Pulleys are nothing but gears without
teeth and instead of running together directly they are made to drive
one another by cords, ropes, cables, or belting of some kinds.
As with gears, the velocities of pulleys are inversely proportional to
Figure 2-8 Belts and pulleys
Pulleys can also be arranged as a block and tackle.
In working out the problems on levers, belts and
pulleys, inclined planes and so forth, we have not taken
account of friction or other sources of energy loss. In other words,
we have supposed them to be perfect, when in fact they are not. To
measure the performance of a machine, we often find its
efficiency, which is defined as
Complete Table of Contents
- = the efficiency
of a machine,
- Win = the input work to a machine, and
- Wout = the output work of a machine.
- 1 Introduction to Mechanisms
- 2 Mechanisms and Simple Machines
- 2.1 The Inclined Plane
- 2.1.1 Screw Jack
- 2.2 Gears
- 2.2.1 Gear Trains
- 2.2.2 Gear Ratios
- 2.3 Belts and Pulleys
- 2.4 Lever
- 2.5 Lever
- 2.6 Wedge
- 2.7 Efficiency of Machines
- 3 More on Machines and Mechanisms
- 4 Basic Kinematics of Constrained Rigid Bodies
- 5 Planar Linkages
- 6 Cams
- 7 Gears
- 8 Other Mechanisms