law of gearing

1. Sanjivani Rural Education Society’s
Sanjivani College of Engineering, Kopargaon-423603
( An Autonomous Institute Affiliated to Savitribai Phule Pune University, Pune)
NAAC ‘A’ Grade Accredited, ISO 9001:2015 Certified
Subject :- Theory of Machines II
T.E. Mechanical (302043)
Unit 1
1.4 Law of Gearing
By
Prof. K. N. Wakchaure(Asst Professor)
Department of Mechanical Engineering
Sanjivani College of Engineering
(An Autonomous Institute)
Kopargaon, Maharashtra
Email: wakchaurekiranmech@Sanjivani.org.in Mobile:- +91-7588025393

2. LAW OF GEARING
 The common normal at the point
of contact between a pair of teeth
must always pass through the
pitch point.
 The angular velocity ratio
between two gears of a gear set
must remain constant
throughout the mesh.
O2
O1
O1
C
N
α
α
β
β
P
M
E
D
Q

3.  Vector QE=V
 Velocity of Gear 1=Vector QC=V1
 Velocity of Gear 2=Vector QD=V2
 V=V1cosα
 V=V1cosβ
 Hence
 V1cosα =V2cosβ
O2
O1
O1
C
N
α
α
β
β
P
M
E
D
Q
C
V2
LAW OF GEARING

4.  V1cosα =V2cosβ
O2
O1
O1
C
N
α
α
β
β
P
M
E
D
Q
C
V2
LAW OF GEARING

5. LAW OF GEARING
 from similar triangles O1MP and O2NP,
 Combining equations (i) and (ii), we have
O2
O1
O1
C
N
α
α
β
β
P
M
E
D
Q
C
V2
The common normal at the point of contact between a pair of teeth
must always pass through the pitch point.
This is the fundamental condition which must be satisfied while
designing the profiles for the teeth of gear wheels. It is also known as
law of gearing.
The angular velocity ratio is inversely proportional to the ratio of the
distances of the point P from the centres O1 and O2, or
the common normal to the two surfaces at the point of contact Q
intersects the line of centres at point P which divides the centre
distance inversely as the ratio of angular velocities.

7. 7PROF. K N WAKCHAURE
Subject :- Theory of Machines II