Processing & Properties of Floor and Wall Tiles.pptx
ย
3.2 KINEMATIC ANALYSIS ON GEAR TRAIN
1. Sanjivani Rural Education Societyโs
Sanjivani College of Engineering, Kopargaon-423603
( An Autonomous Institute Affiliated to Savitribai Phule Pune University, Pune)
NAAC โAโ Grade Accredited, ISO 9001:2015 Certified
Subject :- Theory of Machines II
T.E. Mechanical (302043)
Unit 3
3.2 Kinematic Analysis of Epicyclic Gear Train
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. Sun Gear= Rotates about own axis
Arm= Rotates about the axis of sun
gear at one end and another end
consist of Planet gear/s
โข Mounted on another shaft
Planet Gear= Rotates about the
own axis as we all over the
periphery of Sun Gear (Epicyclic
action)
EPICYCLIC GEAR TRAIN
Sun Gear
Planet Gear
Arm
3. Kinematic Analysis (Tabular Method)
Gear A
Gear B
Arm C
Condition 1: ARM C is fixed and gear A competes +1 rotation (Clockwise)
๐ต ๐ช= 0
๐ต ๐จ= + 1
๐ต ๐ฉ
๐ต ๐จ
=
๐ ๐
๐ ๐
๐ต ๐ฉ =
๐ ๐
๐ ๐
โข Gear A and Gear B are having External Meshing.
โข hence Gear A and Gear B will be rotate in opposite direction.
โข As gear A rotation in Clockwise direction, gear B will move in
Anticlockwise direction.
๐ฏ๐๐๐๐ ๐ต ๐ฉ = โ
๐ ๐
๐ ๐
4. Kinematic Analysis (Tabular Method)
Gear A
Gear B
Arm C
Condition 2: ARM C is fixed and gear A competes +๐ rotation
(Clockwise)
๐ต ๐ช= 0
๐ต ๐จ= + ๐
๐ต ๐ฉ
๐ต ๐จ
=
๐ ๐
๐ ๐
๐ต ๐ฉ =
๐ ๐
๐ ๐
โ ๐
โข Gear A and Gear B are having External Meshing.
โข hence Gear A and Gear B will be rotate in opposite direction.
โข As gear A rotation in Clockwise direction, gear B will move in
Anticlockwise direction.
๐ต ๐ฉ = โ
๐ ๐
๐ ๐
โ ๐
5. Kinematic Analysis (Tabular Method)
Gear A
Gear B
Arm C
Condition 3: ARM C moving with +y rotation
๐ต ๐ช= +y
โข As arm C rotates which add +y rotations in the speed of Gear
A and Gear B
6. Kinematic Analysis (Tabular Method)
Gear A
Gear B
Arm C
STEP OPERATION
SPEED OF THE ELEMENTS
ARM C GEAR A GEAR B
1 ARM C is fixed and gear A competes +1
rotation
0 +1
-
๐ ๐
๐ ๐
2 ARM C is fixed and gear A competes +x
rotation
0 +x
- ๐ฑ โ
๐ ๐
๐ ๐
3 Add +y rotation of ARM C +y +y +y
4 Add Step 2 +Step 3 ๐ฒ x+y
y - ๐ฑ โ
๐ ๐
๐ ๐
๐ต ๐ฉ = ๐ โ
๐ ๐
๐ ๐
โ ๐
๐ต ๐ช = +๐
๐ต ๐จ = ๐ + ๐
7. Ref. https://nptel.ac.in/courses/116/102/116102012/
Kinematic Analysis (Tabular Method)
STEP OPERATION
SPEED OF THE ELEMENTS
ARM C GEAR A GEAR B
1
ARM C is fixed and gear A competes
+1 rotation
0 +1 -
๐ ๐
๐ ๐
2
ARM C is fixed and gear A competes
+x rotation
0 +x - ๐ฑ โ
๐ ๐
๐ ๐
3 Add +y rotation of ARM C +y +y +y
4 Add Step 2 +Step 3 ๐ฒ x+y y - ๐ฑ โ
๐ ๐
๐ ๐
๐ฎ๐๐๐๐ ๐ ๐ = ๐ ๐ฉ = ๐๐
๐ต ๐ฉ = ๐ โ
๐ ๐
๐ ๐
โ ๐๐ต ๐ช = +๐ ๐ต ๐จ = ๐ + ๐
๐ต ๐ช = +๐ ๐ต ๐จ = ๐
๐ + ๐ = ๐๐ต ๐ช = ๐ = ๐ ๐ = โ๐ ๐ = โ๐
๐ต ๐ฉ = ๐ โ
๐ ๐
๐ ๐
โ ๐ ๐ต ๐ฉ = ๐ โ
๐๐
๐๐
โ (โ๐) ๐ต ๐ฉ=2
๐ต ๐ช = +๐ ๐ต ๐จ = ๐
8. Ref. https://nptel.ac.in/courses/116/102/116102012/
Kinematic Analysis (Tabular Method)
STEP OPERATION
SPEED OF THE ELEMENTS
ARM C GEAR A GEAR B
1
ARM C is fixed and gear A competes
+1 rotation
0 +1 -
๐ ๐
๐ ๐
2
ARM C is fixed and gear A competes
+x rotation
0 +x - ๐ฑ โ
๐ ๐
๐ ๐
3 Add +y rotation of ARM C +y +y +y
4 Add Step 2 +Step 3 ๐ฒ x+y y - ๐ฑ โ
๐ ๐
๐ ๐
๐ฎ๐๐๐๐ ๐ ๐ = ๐ ๐ฉ = ๐๐
๐ต ๐ฉ = ๐ โ
๐ ๐
๐ ๐
โ ๐๐ต ๐ช = +๐ ๐ต ๐จ = ๐ + ๐
๐ต ๐ช = +๐ ๐ต ๐จ = ๐
๐ + ๐ = ๐๐ต ๐ช = ๐ = ๐ ๐ = ๐ โ ๐ ๐ = ๐
๐ต ๐ฉ = ๐ โ
๐ ๐
๐ ๐
โ ๐ ๐ต ๐ฉ = ๐ โ
๐๐
๐๐
โ (๐) ๐ต ๐ฉ=1
๐ต ๐จ = ๐ ๐ต ๐ช = +๐
9. Ref. https://nptel.ac.in/courses/116/102/116102012/
Kinematic Analysis (Tabular Method)
STEP OPERATION
SPEED OF THE ELEMENTS
ARM C GEAR A GEAR B
1
ARM C is fixed and gear A competes
+1 rotation
0 +1 -
๐ ๐
๐ ๐
2
ARM C is fixed and gear A competes
+x rotation
0 +x - ๐ฑ โ
๐ ๐
๐ ๐
3 Add +y rotation of ARM C +y +y +y
4 Add Step 2 +Step 3 ๐ฒ x+y y - ๐ฑ โ
๐ ๐
๐ ๐
๐ฎ๐๐๐๐ ๐ ๐ = ๐ ๐ฉ = ๐๐
๐ต ๐ฉ = ๐ โ
๐ ๐
๐ ๐
โ ๐๐ต ๐ช = +๐ ๐ต ๐จ = ๐ + ๐
๐ต ๐ช = +๐ ๐ต ๐จ = โ๐
๐ + ๐ = โ๐๐ต ๐ช = ๐ = ๐ ๐ = โ๐ โ ๐ ๐ = โ๐
๐ต ๐ฉ = ๐ โ
๐ ๐
๐ ๐
โ ๐ ๐ต ๐ฉ = ๐ โ
๐๐
๐๐
โ (โ๐) ๐ต ๐ฉ=3
๐ต ๐จ = โ๐ ๐ต ๐ช = +๐