Prepared for a presentation as part of curriculum

1. Kinematics of Machine -
Gears
Adhav Ravi Barathwaj
Semester IV / 2024 – Mechatronics- SASTRA

2. The Context kinematics refers to the study of the motion of
points, objects, and group of objects while ignoring
the causes of its motion
Key Terms
• kinematics: The branch of mechanics concerned
with objects in motion, but not with the forces
involved.
• displacement: A vector quantity that denotes
distance with a directional component.
• frame of reference: A coordinate system or set of
axes within which to measure the position,
orientation, and other properties of objects in it.
• scalar: A quantity that has magnitude but not
direction; compare vector.
• vector: A directed quantity, one with both
magnitude and direction; the between two
points.
This Brief Presentation will cover high level aspects Gears, and few calculations wit respect to Unit IV

3. Gears and Gear Trains
• Gears are wheel-like machine elements that have
teeth uniformly spaced around the outer surface. They
are always used in pairs.
• Gears are mounted on rotatable shafts and the teeth
are made to mesh (engage) with a gear that is on another
shaft.
4 Major Uses of gears
• Regulate Speed * force * Steer Rotation Direction *
Control Movement
• A gear train is a series of interlinked wheels used in
engines for generating power. It has no influence on
the input or output of the motion.
• It is an assembly of gears arranged so that the output
of one gear (the driver) becomes the input of another
gear (the driven gear).
Picture Courtesy - https://www.engineersgallery.com/gears-and-its-types/

4. Interference and Undercutting - Terminologies
If the involute portion of the touches the non-involute portion
of the gear, there is involute to non-involute interaction
between the mating gears and the law of gearing will not be
satisfied, this situation is called interference in the gears
Possible ways to prevent interference in gears are :
• Stubbing the teeth decreases the path of contact and contact ratio,
thereby decreasing interference.
• Undercutting of gear eliminates interference however gear becomes
weaker.
• Increasing pressure angle decreases interference.
• Increasing the number of teeth decreases interference.
• Addendum of gear can be modified.
• Circular pitch can be increased.
• Decreasing the addendum of gear and by increasing the same for
pinion.
Picture Courtesy: https://www.slideshare.net/slideshow/gears-14683061/14683061

5. What is Length of Path of Contact in a gear
wheel?
▪ In an involute gear, the portion of the line of action that sees actual
contact is its length of the path of contact.
▪ a and b are the points ( Note the ) where the tooth tip circle starts to
intersect the line of action and where the contact ends respectively.
This distance a bis the length of the path of contact.
• Here, line a bis Length of path of contact
• Line a p is path of approach
• Line p bis path of recess
Courtesy: https://www.khkgreas.us

6. What is a Base Pitch?
Courtesy: https://www.tec-science.com/mechanical-power-transmission/involute-gear/geometry-of-involute-gears/
All involutes of a gear are equidistant to each other
The base pitch corresponds to the distance between two
meshing flanks and results from the right-angled distance
between two adjacent involutes. . In other words, it is the
space between the teeth.
The circumference of the base circle divided by the number
of teeth, is called the BASE PITCH.
If pitch circle diameter D and number of teeth T. The circular
pitch of the gear is
Base Pitch = Circular Pitch x Cosine of the pressure angle
(PA)
This base pitch is equal to the normal pitch.

7. Contact Ratio
CONTACT RATIO (NUMBER OF PAIRS OF TEETH IN CONTACT)
• The contact ratio is a measure of overlapping tooth action which is necessary to assure smooth,
continuous action and Quite working of gears
• It is defined as the ratio of the length of the arc of contact to the circular pitch.
• The contact ratio, usually, is not a whole number.
• What is the best contact ratio?
• It is good practice to maintain a contact ratio of 1.2 or greater.
Contact Ratio ε
ε = the length of the path of contact / base pitch
• Higher the contact ratio better will be the carrying capacity, making contact between teeth smoother
and softer, thereby reduce vibration and noise and impact on the systems.

8. Further Reading and References
• Types of Gears –
• https://www.iqsdirectory.com/articles/gear/types-of-gears.html
• https://waykenrm.com/blogs/types-of-gears/
• Contact Ratio of Gears, Tooth Modifications, and the Relationship Among The Gears - https://www.sdp-
si.com/resources/elements-of-metric-gear-technology/page6.php
• The importance of contact ratios, How to calculate the contact ratios for various styles of gearing -
https://gearsolutions.com/departments/tooth-tips/the-importance-of-contact-ratios/
• Design of Spur Gears Using Profile Modification -
https://www.researchgate.net/publication/276880143_Design_of_Spur_Gears_Using_Profile_Modification/fi
gures?lo=1