kinematics of machinery - introduction
DESCRIPTION
Basic definitions of link, kinematic pair, kinematic chain, Degree of freedom.TRANSCRIPT
![Page 1: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/1.jpg)
INTRODUCTION
![Page 2: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/2.jpg)
Kinematics: The study of motion without regard to forces.
Kinetics: The study of forces on systems in motion.
![Page 3: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/3.jpg)
DIAGRAM SHOWING LATHE PARTS
![Page 4: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/4.jpg)
![Page 5: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/5.jpg)
THE SHAPER
![Page 6: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/6.jpg)
![Page 7: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/7.jpg)
![Page 8: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/8.jpg)
Number of links, L = 12,
12 11
10
98
7
6
5
1
2
3
4
11, 12
1
2
3
4
56
78
9
10
![Page 9: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/9.jpg)
![Page 10: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/10.jpg)
Mechanism: A system of elements arranged to transmit motion in a predetermined fashion.
Machine : A system of elements arranged to transmit motion and energy in a predetermined fashion.
Mechanism can also be defined as a device that transforms motion to some desirable pattern and typically develops very low forces and transmits little power.
Virtually any machine or device that moves contains one or more kinematic elements such as links, gears, cams, belts, chains.
![Page 11: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/11.jpg)
![Page 12: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/12.jpg)
![Page 13: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/13.jpg)
Mechanism: A combination of no. of bodies (usually resistant bodies) assembled in such a way that the motion of one causes constrained and predictable motion to the others is known as a mechanism.
A mechanism is made of no. of resistant bodies out of which some have relative to the others.
![Page 14: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/14.jpg)
Link: A resistant body or a group of resistant bodies (with no relative motion among them) of a mechanism, connecting other members and having motion relative to them is called a kinematic link.
(or)
A link is a rigid body that possesses at least 2 nodes that are points of attachment to other links
Types:
1. Binary link – 2nodes2. Ternary link3. Quaternary link
![Page 15: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/15.jpg)
Kinematic pair: A kinematic pair or simply a pair is a joint of 2 links having relative motion between them.
Classification: Based on
1. Nature of contact : Lower and higher pairs
2. Nature of Mechanical constraint : Closed and unclosed pair
3. Nature of relative motion
4. No. of DOF
![Page 16: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/16.jpg)
![Page 17: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/17.jpg)
Based on nature of relative motion:
![Page 18: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/18.jpg)
![Page 19: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/19.jpg)
Based on nature of mechanical constarint:1. Closed pair or form closed pair2. Unclosed pair or force closed pair
![Page 20: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/20.jpg)
![Page 21: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/21.jpg)
![Page 22: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/22.jpg)
![Page 23: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/23.jpg)
Kinematic chain:
A Kinematic chain is an assembly of links in which the relative motion of the links is possible and the motion of each relative to the other is definite.
Linkage
Mechanism
![Page 24: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/24.jpg)
![Page 25: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/25.jpg)
Kinematic chain:
A Kinematic chain is an assembly of links in which the relative motion of the links is possible and the motion of each relative to the other is definite.
Linkage: If one of the links of a KC is fixed to the ground
Mechanism: If motion of any one of the links results in definite motion of the others.
![Page 26: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/26.jpg)
26
Surface contact pairs are lower pairs.
The commonly used lower pairs include
(1) Revolute Pair
(2) Prismatic Pair
(3) Screw Pair
(4) Cylindrical Pair
(5) Spherical Pair
(6) Planar Pair
LOWER KINEMATIC PAIRS
![Page 27: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/27.jpg)
27
Degrees of freedom: 1 Symbol: P Relative motion: linear
PRISMATIC PAIR (SLIDER JOINT)
![Page 28: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/28.jpg)
28
Degrees of freedom: 1 Symbol: H Relative motion: Helical
SCREW PAIR (HELICAL PAIR)
![Page 29: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/29.jpg)
29
Degrees of freedom: 2 Symbol: C Relative motion: Cylindrical
CYLINDRICAL PAIR
![Page 30: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/30.jpg)
30
Degrees of freedom: 3 Symbol: S Relative motion: Spherical
SPHERICAL PAIR (GLOBULAR PAIR)
![Page 31: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/31.jpg)
31
Degrees of freedom: 3 Symbol: F Relative motion: Planar
PLANAR PAIR (FLAT PAIR)
![Page 32: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/32.jpg)
32
Higher pairs (joints) have either a line contact or a point contact.
Higher pairs exist in cam mechanisms, gear trains, ball and roller bearings and roll-slide joints, etc.
For planar motion, both line contact higher pairs and point contact higher pairs have two degrees-of-freedom.
The only constraint at the contact point is along the common normal.
A pin-in-slot joint (rolling contact with sliding) is also a higher pair with a line contact between the pin and the slot.
HIGHER KINEMATIC PAIRS
![Page 33: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/33.jpg)
33
HIGHER KINEMATIC PAIRS
higher.SLDASM
![Page 34: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/34.jpg)
Linkage: If one of the links of a KC is fixed to the ground
Mechanism: If motion of any one of the links results in definite motion of the others.
![Page 35: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/35.jpg)
Degrees of freedom
General defn: The DOF of a body is equal to the no. of independent coordinates required to specify its position.
![Page 36: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/36.jpg)
Spatial D.O.F. Planar D.O.F.
R – Pair P – Pair C - Pair
![Page 37: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/37.jpg)
For a Link – Six in spatial motion, three in planar motion.
For a Kinematic Pair –
Number of independent co-ordinates/pair variables to specify the position of one link with another link
(OR)
Number of independent relative motions possible between the links. Maximum five and minimum one in spatial motion. Maximum two and minimum one in planar motion.
![Page 38: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/38.jpg)
![Page 39: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/39.jpg)
Kinematic chain:
A Kinematic chain is an assembly of links in which the relative motion of the links is possible and the motion of each relative to the other is definite.
A closed chain is a consecutive set of links in which the last link is connected to the first.
An open chain is the one in which the last link is not connected to the first link.
A closed chain mechanism. An open chain
mechanism.
![Page 40: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/40.jpg)
40
KINEMATIC CHAIN CLOSED
5 bar linkage.SLDASM
Ground
Slider-crank
![Page 41: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/41.jpg)
41
KINEMATIC CHAIN OPEN
fanuc robot.SLDASM
Ground
![Page 42: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/42.jpg)
Degrees of freedom/Mobility of a mechanism
• No. of inputs required to get a constrained mechanism (or) no. of position variables needed to sketch the mechanism with all link lengths known.
![Page 43: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/43.jpg)
Ken Youssefi Mechanical & Aerospace Engineering Dept., SJSU
43
DEGREES OF FREEDOM (DOF)
Kutzbach’s (modified Grubler) equation
DOF ≤ 0 structure
mechanismDOF > 0
• F = 3(n-1)-2P1-1P2
• F – D.O.F n – No. of links
• P1 – No. of kinematic pairs with 1 D.O.F.
• P2 – No. of kinematic pairs with 2 D.O.F.
![Page 44: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/44.jpg)
![Page 45: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/45.jpg)
![Page 46: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/46.jpg)
![Page 47: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/47.jpg)
Exception’s
![Page 48: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/48.jpg)
![Page 49: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/49.jpg)
![Page 50: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/50.jpg)
![Page 51: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/51.jpg)
![Page 52: Kinematics of Machinery - Introduction](https://reader036.vdocuments.us/reader036/viewer/2022081419/55cf9818550346d033959003/html5/thumbnails/52.jpg)