ME 44 Kinematics of Machines

1
ME 44Kinematics of Machines
Chapter 4 Spur Gears
Gears Gears are machine elements that transmit
motion by means of successively engaging teeth.
The gear teeth act like small levers.
Dr.T.V.Govindaraju,SSEC
2
Power transmission systems
Belt/Rope Drives - Large center distance of
the shafts
Chain Drives - Medium center distance
of the shafts
Gear Drives - Small center distance
of the shafts
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3
Friction Discs
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Spur Gears animation
http//www.drgears.com/gearanims.htm
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Bevel Gears animation
http//www.drgears.com/gearanims.htm
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Applications animation
Conveyor/Counting
Gear train
Gear Pump
Watch gear wheels
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Industrial Applications
 
Diesel engine builders
Printing machinery parts
Rotary die cutting machines
Hoists and Cranes
Blow molding machinery
Boat out drives
Agricultural equipment
Automotive prototype and reproduction
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Industrial Applications
 
Newspaper Industry
Plastics machinery

Motorcycle Transmissions
Polymer pumps Automotive applications Commercial
and Military operations Special gear box
builders
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Industrial Applications
 
Heavy earth moving vehicles Canning and
bottling machinery builders Special machine
tool builders Book binding machines
Marine applications Injection molding
machinery Military off-road vehicles
Stamping presses
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Classification
Gears may be classified according to the relative
position of the axes of revolution. The axes may
be parallel, intersecting and neither parallel
nor intersecting.
1. Gears for connecting parallel shafts
Spur Gears External contact
Internal contact
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Helical gears
Parallel Helical gears Heringbone gears
















(Double Helical gears)
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Bevel gears
2. Gears for connecting intersecting shafts
Bevel Gears
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Bevel gears
http//www.drgears.com/gearanims.htm
Straight bevel gears
Spiral bevel gears
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3. Gears for neither parallel nor intersecting
shafts.
Worm Worm Wheel
Crossed-helical gears
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Rack and Pinion
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Worm and Worm Wheel
http//www.drgears.com/gearanims.htm

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Hypoid Gear
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Hypoid Gear
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Gear Box
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TerminologySpur Gears

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Terminology
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Definitions
Addendum The radial distance between the Pitch
Circle and the top of the teeth. Arc of Action
Is the arc of the Pitch Circle between the
beginning and the end of the engagement of a
given pair of teeth. Arc of Approach Is the arc
of the Pitch Circle between the first point of
contact of the gear teeth and the Pitch Point.
Arc of Recession That arc of the Pitch Circle
between the Pitch Point and the last point of
contact of the gear teeth. Backlash Play
between mating teeth.
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Definitions
Base Circle The circle from which is generated
the involute curve upon which the tooth profile
is based. Center Distance The distance between
centers of two gears. Chordal Addendum The
distance between a chord, passing through the
points where the Pitch Circle crosses the tooth
profile, and the tooth top. Chordal Thickness
The thickness of the tooth measured along a chord
passing through the points where the Pitch Circle
crosses the tooth profile. Circular Pitch
Millimeter of Pitch Circle circumference per
tooth.
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Definitions
Circular Thickness The thickness of the tooth
measured along an arc following the Pitch Circle
Clearance The distance between the top of a
tooth and the bottom of the space into which it
fits on the meshing gear. Contact Ratio The
ratio of the length of the Arc of Action to the
Circular Pitch. Dedendum The radial distance
between the bottom of the tooth to pitch circle.
Diametral Pitch Teeth per mm of diameter.
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Definitions
Face The working surface of a gear tooth,
located between the pitch diameter and the top of
the tooth. Face Width The width of the tooth
measured parallel to the gear axis. Flank The
working surface of a gear tooth, located between
the pitch diameter and the bottom of the teeth
Gear The larger of two meshed gears. If both
gears are the same size, they are both called
"gears". Land The top surface of the tooth.
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Definitions
Line of Action That line along which the point
of contact between gear teeth travels, between
the first point of contact and the last. Module
Millimeter of Pitch Diameter to Teeth. Pinion
The smaller of two meshed gears. Pitch Circle
The circle, the radius of which is equal to the
distance from the center of the gear to the pitch
point. Diametral pitch Teeth per millimeter of
pitch diameter. Pitch Point The point of
tangency of the pitch circles of two meshing
gears, where the Line of Centers crosses the
pitch circles.
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Definitions
Pressure Angle Angle between the Line of Action
and a line perpendicular to the Line of Centers.
Profile Shift An increase in the Outer Diameter
and Root Diameter of a gear, introduced to lower
the practical tooth number or acheive a
non-standard Center Distance. Ratio Ratio of
the numbers of teeth on mating gears. Root
Circle The circle that passes through the bottom
of the tooth spaces. Root Diameter The diameter
of the Root Circle. Working Depth The depth to
which a tooth extends into the space between
teeth on the mating gear.
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Formulae
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Formulae
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Forumulae Specific to Gearswith Standard Teeth
Addendum 1 Diametral Pitch 0.3183
Circular Pitch Dedendum 1.157 Diametral
Pitch 0.3683 Circular Pitch Working
Depth 2 Diametral Pitch 0.6366
Circular Pitch Whole Depth 2.157 Diametral
Pitch 0.6866 Circular Pitch
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Forumulae Specific to Gearswith Standard Teeth
Clearance 0.157 Diametral Pitch 0.05
Circular Pitch Outside Diameter (Teeth 2)
Diametral Pitch (Teeth 2) Circular Pitch
p Diametral Pitch (Teeth 2) Outside
Diameter
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Law of Gearing
Tooth profile 1 drives tooth profile 2 by acting
at the instantaneous contact point K.
?
N1 N2 is the common normal of the two profiles.
N1 is the foot of the perpendicular from O1 to
N1N2
N2 is the foot of the perpendicular from O2 to
N1N2.
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Law of Gearing
Although the two profiles have different
velocities V1 and V2 at point K, their velocities
along N1N2 are equal in both magnitude and
direction. Otherwise the two tooth profiles would
separate from each other. Therefore, we have
?
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Law of Gearing
?
We notice that the intersection of the tangency
N1N2 and the line of center O1O2 is point P, and
from the similar triangles
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Law of Gearing
Therefore, velocity ratio
Point P is very important to the velocity ratio,
and it is called the pitch point. Pitch point
divides the line between the line of centers and
its position decides the velocity ratio of the
two teeth. The above expression is the
fundamental law of gear-tooth action
?
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Law of Gearing
From the equations 4.2 and 4.4, we can write,
?
-ratio of the radii of the two base circles and
also given by
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Law of Gearing
-centre distance between the base circles
?
? pressure angle or the angle of obliquity. It
is angle between the common normal to the base
circles and the common tangent to the pitch
circles.
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Constant Velocity Ratio
A common normal (the line of action) to the tooth
profiles at their point of contact must, in all
positions of the contacting teeth, pass through a
fixed point on the line-of-centers called the
pitch point Any two curves or profiles engaging
each other and satisfying the law of gearing are
conjugate curves, and the relative rotation speed
of the gears will be constant (constant velocity
ratio).
?
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Conjugate Profiles
To obtain the expected velocity ratio of two
tooth profiles, the normal line of their profiles
must pass through the corresponding pitch point,
which is decided by the velocity ratio. The two
profiles which satisfy this requirement are
called conjugate profiles.
?
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Conjugate action
It is essential for correctly meshing gears, the
size of the teeth ( the module ) must be the same
for both the gears. Another requirement - the
shape of teeth necessary for the speed ratio to
remain constant during an increment of rotation
this behaviour of the contacting surfaces (ie.
the teeth flanks) is known as conjugate action.
doug_at_mech.uwa.edu.au
Dr.T.V.Govindaraju,SSEC