Designing and Drawing a Sprocket
Visualizing ideas through the creation of CAD solid models is a key engineering skill. The process designing and drawing a sprocket is an excellent way to incorporate 8th and 9th grade algebra and geometry skills and knowledge. The following text offers the information andprocedural steps necessary to generate the profile of standard pitch sprockets. This process will yield an approximate tooth form that can be used to generate solid models of the sprockets used in the GEARS-IDS kit of parts. The process of producing and saving a solid model library of GEARS-IDS sprockets and parts, provides students and instructors with the opportunity to combine algebra, geometry andtrigonometry knowledge with engineering drawing skills to produce the design elements necessary to fully visualize their mechanical creations.
Fig. 18.104.22.168 Sprocket Tooth Geometry
(Adapted from the American Chain Association Chains for Power Transmission and Material Handling handbook.
GEARS Educational Systems 105 Webster St. Hanover Massachusetts 02339 Tel. 781 878 1512 Fax 781 878 6708www.gearseds.com
Sprocket Tooth Design Formulas
Refer to Fig. 22.214.171.124 Sprocket Tooth Geometry The tooth form of a sprocket is derived from the geometric path described by the chain roller as it moves through the pitch line, and pitch circle for a given sprocket and chain pitch. The shape of the tooth form is mathematically related to the Chain Pitch (P), the Number of Teeth on the Sprocket (N),and the Diameter of the Roller (Dr). The formulas for the seating curve, radius R and the topping curve radius F include the clearances necessary to allow smooth engagement between the chain rollers and sprocket teeth. The following formulas are taken from the American Chain Association Chains for Power Transmission and Material Handling handbook, and they represent the industry standards for thedevelopment of sprocket tooth forms.
P N Dr Ds R A B ac M = Chain Pitch = Number of Teeth = Roller Diameter ( See Table) yz = Dr 1.4 sin(17° −
64 56° ) − 0.8 sin(18° − ) N N
= (Seating curve diameter) = 1.0005 Dr + 0.003 ab = 1.4 Dr
60° N 56° = 18° − N
= 35° + = 0.8 x Dr
= Ds/2 = 0.5025 Dr + 0.0015
W = 1.4 Dr cos
V = 1.4 Dr sin
180° N 56° 64°
= 0.8x Dr cos( 35° +
60° ) N 60° ) N
) + 1.4 cos(17° − F = Dr 0.8 cos(18° − N N
F 2 − (1.4 Dr − P 2 ) 2
= 0.8 x Dr sin ( 35° + = 1.3025 Dr + 0.0015
P 180° 180° cos + H sin 2 N N
P 180° sin N
Chordal Length of Arc xy = (2.605 Dr + 0.003) sin ( 9° −
28° ) N
Additional Sprocket Formulas Outside Diameter of a sprocket when j = 0.3P180° OD = P (0.6 + cot ) N Outside diameter of a sprocket when tooth is pointed OD = P cot
180° 180° + cos ( Ds − Dr ) + 2 H N N
GEARS Educational Systems 105 Webster St. Hanover Massachusetts 02339 Tel. 781 878 1512 Fax 781 878 6708 www.gearseds.com
Procedure for Drawing a Sprocket
In this example we will draw the tooth form for the GEARS-IDS 30 tooth Sprocket. Refer toFig. 126.96.36.199, the Sprocket Formulas and the Maximum Roller Diameter Table.
NOTE: This is primarily an algebra and geometry exercise. The sprocket tooth profile does not need to be drawn perfectly. We will be generating, a mathematical model of the sprocket profile in order to help us draw an approximate model. When drawing the model, do not be overly concerned with arcs that are not exactlytangent to lines, or line lengths that are not exact to 3 or 4 decimal places. Use your drawing tools and common sense in order to create the profile as best you can. Chain Number Pitch Max Roller Diameter 25 ¼ 0.130* 35 3/8 0.200* 41 ½ 0.306 40 ½ 5/16 * This refers to the bushing diameter since the chain pitch is small and rollerless.
Determine the values for P, N and Dr Calculate the...