Lecture 9 Transmission of Power by mechanical means
Mechanisms are planned building blocks of machines that are devices for transmission of power by mechanical means. Mechanisms have versatile applications.
(A) Planar Linkages / Mechanisms
Linkage is a mechanism consisting of Lower Pair(s).
Let us discuss four bar linkage / (planar) mechanism since it is the simplest mechanism that one can think of. To start with, consider a four bar linkage / (planar) mechanism with four revolute pairs(R).
Four bar linkage / (planer) mechanism As
Crank - Lever Mechanism
OR
Crank - Rocker Mechanism :
The four links are numbered,
1 as fixed link ( Frame),
2 as Crank that is connected to the fixed link and makes a complete rotation,
3 as Coupler that connect link 2 and 4 or as motion transfer link between links 2 and 4,
4 as Rocker / Lever.
Crank is rotatably mounted on the frame and can perform complete revolutions. Crank is normally Input Link and nature of its Input Motion that is available is in the form of Continuous Rotation.
Coupler transforms crank motion to lever (rocker arm).
Lever (Rocker) is rotatably mounted on the frame and do not perform complete revolutions. Lever (Rocker) is normally Output Link and its desired Output Motion is that of Continuos to- and fro- Rocking / Oscillating.
Geometric Motion transformations of Four bar linkage / (planer) mechanism:
(1) Rocker - Crank Mechanism
OR
Lever - Crank Mechanism
(2) Crank - Slider Mechanism :
Consider a 4 revolute pair (4R) planar mechanism where the fourth kinematic pair goes to infinity along a vertical direction. Consequently, that fourth kinematic pair is converted to a prismatic pair and what one get is a 3R - 1P [three revolute pair (3R) one prismatic pair (1P)] mechanism. Such a 3R -1P mechanism is known as a Crank - (Offset) Slider Mechanism that is used to convert uniform rotation of link 2 (Crank) into rectilinear to and fro translation of link 4 (Offset Slider).
Note: Offset is perpendicular distance between line of reciprocation of Offset Slider and ground line.
When offset is zero, such 3R - 1P mechanism is known as Crank - Slider Mechanism.
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| Crank-Slider Mechanism |
Link 1 (Frame = Fixed Link) has a revolute pair (R) with link 2 (Crank) at one end and a prismatic pair (P) with link 4 (Slider) at the other end.
Link 3 ( Coupler = Motion Transfer Link) has a revolute pair (R) with link 2 (Crank) at one end and another revolute pair (R) with link 4 (Slider)
Examples of Crank - Slider Mechanism with offset zero are (1) Reciptocating Air Compressor Mechanism and (2) Reciprocating Pump Mechanism wherein Crank [Link - 2] is the Input Link and Slider (Piston) [Link 4] is the Output Link.
First Link = Frame (Fixed Link)
Second link = Sliding element
Third link = Coupler OR Connecting Rod
Fourth link = Crank
Sliding element replaces lever (rocker arm).
Coupler is attached to a sliding element that is Input Link and nature of its Input Motion that is available is in the form of Continuous to and fro translation OR sliding motion.
Coupler transforms sliding motion to crank.
Crank is rotatably mounted on the frame and can perform complete revolutions.
Crank is Output Link and its desired Output Motion is that of Continuos Rotation.
Example: Piston as Sliding Element in an Internal Combustion Engine
Sliding Motion (Linear Motion) of Piston [link - 2] is transformed into Rotary Motion (Angular Motion) of Crank [Link - 4] through Coupler (link - 3).
(4) Crank - Crank [Double Crank] Mechanism
Or
Crank - Drag link - Crank Mechanism
Second link , crank that is shortest link in terms of dimensions is fixed or held stationary, the resulting four bar linkage / (planar) mechanism is Crank - Drag link - Crank Mechanism
1st link= frame = Originally the "crank"[Link 2]
2nd link = crank = Originally the "coupler"[Link 3]
3rd link = coupler = Originally the "rocker"[Link 4]
4th link = crank = Originally the "frame" [Link 1]
2nd link is Input Link and nature of Input Motion that is available of "Driving Crank" ( left side Crank with respect to frame) is Continuous Rotation at constant angular speed.
4th link is Output Link and desired Output Motion of "Driven Crank" ( right side Crank with respect to frame) is Continuous Rotation at varying angular speed
Note: Coupler (Revised 3rd link ) is the drag link.
(5) Rocker - Rocker [Double Rocker] Mechanism
(6) Double Slider Mechanism :
Example - Scotch yoke mechanism
Scotch yoke mechanism is a variation of Crank - Slider Mechanism (Variation of 2nd Geometric Motion Transformation of Four bar linkage / (planar) mechanism with coupler of infinite length and follower as sliding element).
Note:
Link - 1 = Frame (Originally Sliding Element)
Link - 2 = Crank (Originally Frame)
Link - 3 = Sliding Element (as Coupler and Sliding Element other than Revised Frame)
Link - 4 =Follower Link with two slots perpendicular to each other ( Originally Connecting Rod of Crank-Slider Mechanism that has infinite length).
The Scotch-Yoke mechanism converts uniform rotary motion into pure Simple Hormonic Motion (SHM).