Robotic Mechanisms – SPUR GEARS 51031
Spur gears or straightcut gears are the simplest type of gear. They consist of a cylinder or disk with the teeth projecting radially, and although they are not straightsided in form, the edge of each tooth is straight and aligned parallel to the axis of rotation. These gears can be meshed together correctly only if they are fitted to parallel shafts.
Spur Gears are Used to Control Power Transmission in These Ways
1. Changing the direction through which power is transmitted (i.e. parallel, right angles, rotating, linear etc.)
2. Changing the amount of force or torque
3. Changing RPM
Spur Gears, are cogged wheels whose cogs or teeth project radially and stand parallel to the axis.
TECHNICAL DETAILS of SPUR GEARS
Diametral Pitch of Spur Gears (DP)
The Diametral Pitch describes the gear tooth size. The Diametral Pitch is expressed as the number of teeth per inch of Pitch Diameter. Larger gears have fewer teeth per inch of Diametral Pitch. Another way of saying this; Gear teeth size varies inversely with Diametral Pitch.
Pitch Diameter of Spur Gears (D)
The Pitch Diameter refers to the diameter of the pitch circle. If the gear pitch is known then the Pitch Diameter is easily calculated using the following formula;
P = N/P
PD = Pitch Diameter, N = Number of teeth on the gear, P = Diametral Pitch (Gear Size)
PD = N/P = 36 /24 = 1,5″
The Pitch Diameter is used to generate the Pitch Circle.
The Pitch Circle
The pitch circle is the geometrical starting point for designing gears and gear trains. Gear trains refer to systems of two or more meshing gears. The pitch circle is an imaginary circle that contacts the pitch circle of any other gear with which it is in mesh. The pitch circle centers are used to ensure accurate centertocenter spacing of meshing gears.
SPUR GEAR IDEAS
Intermittent Motion Spur Gear
MAKING SPUR GEARS
Broaching External Spur Gears on Lathe
Gear Making – Cutting a Spur Gear for the AL54B Lathe
Making Plastic Spur Gears
GEAR TERMS
Addendum (A): The addendum refers to the distance from the top of the tooth to the Pitch circle.
Dedendum (B): The Dedendum refers to the distance from the Pitch circle to the root circle.
Clearance (C) : Refers to the radial distance between the top and bottom of gears in mesh. Some machinists and mechanics refer to clearance as “play” or the degree of looseness between mating parts.
Whole Depth (WD) : Refers to the distance from the top of the tooth to the bottom of the tooth.
Pressure Angle (PA) (Choose either 14.5 or 20 degrees) : The pressure angle figures into the geometry or form of the gear tooth. It refers to the angle through which forces are transmitted between meshing gears. 14.5degree tooth forms were the original “standard” gear design. While they are still widely available, the 20degree PA gear tooth forms have wider bases and can transmit greater loads. Note: 14.5degree PA tooth forms will not mesh with 20degree PA teeth. Be certain to verify the Pressure angle of the gears you use.
Center Distance : The center distance of 2 spur gears is the distance from the center shaft of one spur gear to the center shaft of the other.
Spur Gear Calculations – Formulas
This is a chart of formulas used in calculating spur gear information based on standard gearing practices.
The spur gear formulas here are based on the “Diametral Pitch system (DP).
These formulas can be used with Circular Pitch and Module systems by first converting them to the Diametral Pitch
To convert a Circular Pitch (CP) to DP – Divide 3.1416 by the circular pitch
To convert the Module (Mod) to DP  Divide the 25.4 by the module
Diametral Pitch  The circular pitch  Divide 3.1416 by the circular pitch 
P_{d} = 3.1416 / CP 
Diametral Pitch 

Divide the number of teeth by the pitch diameter 
P_{d} = N / D 
Diametral Pitch 

Divide number of teeth + 2 by the outside diameter 
P_{d} = (N+2) / OD 
Diametral Pitch 

Divide the base pitch by the cosine of the pressure angle then divide by 3.1416 
P_{d} = (BP / Cos PA) / 3.1416 
Pitch Diameter 

Divide the number of teeth by the diametral pitch 
D = N / P_{d} 
Pitch Diameter 

Divide the product of the outside diameter + number of teeth by the number of teeth + 2 
D = (OD x N) / (N+2) 
Pitch Diameter 

Subtract 2 divided by the diametral pitch from the outside diameter 
D = OD – (2/ P_{d}) 
Pitch Diameter 

Multiply addendum by the number of teeth 
D = A x N 
Pitch Diameter 

Divide the base diameter by the cosine of the pressure angle 
D = BD / (Cos Pa) 
Outside Diameter 

Divide number of teeth + 2 by the diametral pitch 
OD = (N+2) / P_{d} 
Outside Diameter 

Two divided by the diametral pitch plus pitch diameter 
OD = (2 / P_{d}) + D 
Outside Diameter 

Number of teeth + 2, divided by the quotient of number of teeth divided by the pitch diameter 
OD = (N+2) / (N / D) 
Outside Diameter 

Multiply the number of teeth + 2 by the addendum 
OD = (N + 2) x A 
Number Of Teeth 

Multiply the pitch diameter by the diametral pitch 
N = D x P_{d} 
Number Of Teeth 

Multiply the outside diameter by the diametral pitch and subtract 2 
N = (OD x P_{d}) – 2 
Thickness Of Tooth 

Divide 1.5708 by the diametral pitch 
t = 1.5708 / P_{d} 
Addendum 

Divide 1 by the diametral pitch 
a = 1 / P_{d} 
Dedendum 

Divide 1.157 (or 1.25) by the diametral pitch 
b = 1.157 / P_{d} 
Working Depth 

Divide 2 by the diametral pitch 
hk = 2 / P_{d} 
Whole Depth 

Divide 2.157 (or 2.25) by the diametral pitch 
ht = 2.157 / P_{d} 
Clearance 

Divide .157 (or .250) by the diametral pitch 
c = .157 / P_{d} 
Clearance 

Divide thickness of tooth at the pitchline by 10 
c = t / 10 
Operating Diametral Pitch 

Add the number of teeth in both gears and divide by 2 then divide by the center distance 
P_{dO} = ((n1 + n2)/2) / C 
Center Distance 

Add the number of teeth in both gears and divide by 2 then divide by the normal diametral pitch 
C = ((n1 + n2)/2) / P_{nd} 
Operating Center Distance 

Add the number of teeth in both gears and divide by 2 then divide by the operating diametral pitch 
Co = ((n1 + n2)/2) / P_{od} 
Base Diameter 

Multiply the pitch diameter by the cosine of the pressure angle 
Db = PD x (cos PA) 
Pressure Angle 

Divide the base diameter by the pitch diameter 
cosPA = Db / D 
Pressure Angle 

Divide Pi by the diametral pitch, then divide by the base pitch 
cosPA = (3.1416 / P_{d}) / Pb 
Base Pitch 

Divide the diametral pitch by Pi, then multiply by the cosine of the pressure angle 
Pb = (P_{d} / 3.1416) x (cos PA) 
Spur Gear Materials
174 PH Stainless Steel
Type 174PH (“precipitationhardening”) stainless steel is arguably the most common of stainless steels. This type of stainless steel has a high level of strength and a moderate level of corrosion resistance.
Type 174PH stainless steel can be found in a wide variety of applications including medical devices, aerospace platforms, as well as chemical and food processing.
303 Stainless Steel
Type 303 Stainless Steel is another popular form of stainless steel that posses nonmagnetic properties. This type of stainless steel is strong, but not as strong as 174PH, and it cannot be heattreated.
Type 303 stainless steel has a high level of resistance to corrosion, and is popular with applications involving surgical devices.
Aluminum Anodized
To guard against oxidation, aluminum can be strengthened and be made more durable through the anodizing process. This process involved placing the material in a chemical bath. After an electric is passed, a coating for “anodized aluminum” is formed, thus provided increased durability.
Brass
Brass is a metal that is an alloy of copper and zinc. Brass is commonly used in applications where low friction is required. Hence, using brass for gear manufacturing is popular. However, brass is much more susceptible to stress fractures than stainless steel.
Cast Polyurethane
Cast Polyurethane is advantageous in that it can be shaped into virtually any kind of shape. It is one of the strongest and abrasiveresistant elastomers available. Cast polyurethane can be developed with varying levels of coefficients of friction, be made flame resistant, and can be made to be flexible at very low temperatures.