0N1·01=O2N202 88品 0n01 mr= m202N20,P The fundamental law of gearing: The angular velocity ratio between the gears of a gearset remains constant throughout the mesh. out 0202N202P =const. @in ⊙1 ON OP
The fundamental law of gearing: The angular velocity ratio between the gears of a gearset remains constant throughout the mesh. O P O P O N O N m in out V 1 2 1 1 2 2 1 2 = = = = O P O P O N O N T T m out i n i n out T 2 1 2 2 1 1 2 1 = = = = = r1 r2 . 1 2 1 1 2 2 1 2 const O P O P O N O N m i n out V = = = = = 1 1 1 2 2 2 O N = O N
Point P is very important to the velocity ratio, and it is called the pitch point. For a constant velocity ratio,the position of P should remain unchanged. -The motion transmission between two gears is equivalent to the motion transmission between two imagined slipless cylinders with radius r,and r2 or diameter d,and d2 -Two circles whose centers are at O,and 0, and through pitch point Pare termed pitch circles Pitch circles Pitch point Pitch circle Constant Angular Velocity Ratio
▪ Point P is very important to the velocity ratio, and it is called the pitch point. ▪ For a constant velocity ratio, the position of P should remain unchanged. ▪ The motion transmission between two gears is equivalent to the motion transmission between two imagined slipless cylinders with radius r1 and r2 or diameter d1 and d2 . ▪Two circles whose centers are at O1 and O2 , and through pitch point P are termed pitch circles. Pitch circles r1 r2 Pitch point Pitch circle Constant Angular Velocity Ratio P
2.The Involute Tooth Form The involute curve is the path What is the involute? traced by a point on a line as How does the involute form? the line rolls without slipping on the circumference of a circle.It may also be defined as a path traced by the end of a 发生线 string which is originally 渐开线 wrapped on a circle when the involute string is unwrapped from the circle.The circle from which A the involute is derived is called the base circle Base circle
2. The Involute Tooth Form The involute curve is the path traced by a point on a line as the line rolls without slipping on the circumference of a circle. It may also be defined as a path traced by the end of a string which is originally wrapped on a circle when the string is unwrapped from the circle. The circle from which the involute is derived is called the base circle. What is the involute? How does the involute form? involute Base circle
2.The Involute Tooth Form The line(string)is always tangent to the basic circle. 2. The center of curvature of the involute is always at the point of tangency of the string with 发生线 the cylinder. 3. A tangency to the involute is 渐开线 then always normal to the involute string,the length of which is y the instantaneous radius of curvature of the involute curve. KB-AB base circle 4.There is no involute curve within the base circle
2. The Involute Tooth Form involute base circle 1. The line(string) is always tangent to the basic circle. 4. There is no involute curve within the base circle. 2. The center of curvature of the involute is always at the point of tangency of the string with the cylinder. 3. A tangency to the involute is then always normal to the string, the length of which is the instantaneous radius of curvature of the involute curve
2.The Involute Tooth Form Involute i function 发生线 rk= 渐开线 COSQ involute 0=invak=tanak-a A base circle
2. The Involute Tooth Form involute base circle Involute function k k k k k b k inv r r = = − = tan cos