The document discusses limiting positions, displacement diagrams, and coupler curves in mechanisms. It defines limiting positions as the extreme locations of an output link's motion path. A stroke is the displacement between two limiting positions. Displacement diagrams graphically show the motion of components over a full cycle. Coupler curves represent the path generated by a point on a linkage coupler as it moves, which can be used to generate complex motion. Examples of determining slider stroke, throw, and generating coupler curves are provided.
4. Limiting Positions
The output link of a mechanism is at a
limiting position when it is placed at an
extreme location along its motion path.
There are normally two limiting positions in
a linkage.
The displacement between two limiting
positions is called a stroke.
The displacement of the stroke can be
linear or angular.
25. STROKE
limiting position 2
limiting position 1
Note that the limiting positions of the rocker are achieved when the
crank and the coupler are in line.
26. Offset Slider-Crank
12
43
22
What is the stroke of the slider driven by the 12-mm crank through a
43-mm link. The slider has an offset of 22 mm from the crank centre
27. Offset Slider-Crank
43-12
22
What is the stroke of the slider driven by the 12-mm crank through a
43-mm link. The slider has an offset of 22 mm from the crank centre.
Lmin
The extreme left
position of the slider
28. Offset Slider-Crank
43+12
22
What is the stroke of the slider driven by the 12-mm crank through a
43-mm link. The slider has an offset of 22 mm from the crank centre.
Lmax
The extreme right
position of the slider
29. Offset Slider-Crank
55
22
What is the stroke of the slider driven by the 12-mm crank
through a 43-mm link. The slider has an offset of 22 mm from the
crank centre.
31
Stroke = Lmax - Lmin
= √(552-222) - √(312-222) = 50.4 - 21.8 = 28.6 mm
Lmin
Lmax
30. Throw Determination by Analytical
Method
Analytically calculate the maximum angular
displacement (‘throw’) of the ram for the crushing
mechanism.
180
420
360
60
ram
crank
31. Throw Determination by Analytical Method
Analytically calculate the maximum angular
displacement (‘throw’) of the ram for the crushing
mechanism. The angular limits are achieved when the
coupler and the crank are in line.
180
420
360
60
throw
32. Throw Determination by Analytical Method
The throw of the ram is the difference between
α1 and α2.
180
360
180
360
α1
α2
α1 = cos-1(1802+3602-4802)
2(180)(360)
= 121.9˚
α2 = cos-1(1802+3602-3602)
2(180)(360)
= 75.5˚
α = α1 – α2
= 121.9˚-75.5˚ = 46.4˚
33. Displacement Diagram for
a Complete Cycle
Motion of a mechanism is normally cyclical especially when the
input motion actuator is a motor that rotate in a single direction.
All components of the mechanism move in phase to assume
different configurations. The mechanism is said to have completed
a cycle when it assumes its original configuration.
More practical to perform complete cycle analysis by using
computerized analytical method rather than graphical because the
tasks are repetitive and too tedious to be performed in the latter.
34. Displacement Diagram
This diagram can be drawn after performing position
analysis for a complete cycle of a mechanism.
The information from the diagram is more reliable if the
analysis is performed at greater number of points, so
analytical method is more practical for this purpose
compared to graphical.
Slider
displacement
diagram for a full
revolution of the
crank.
Crank angle (deg)
Slider
position
(mm)
35. Coupler Curves
Curve generated by a point on a link, normally the coupler of a
4-bar linkage, as the linkage moves
Simple solution to generate complex motion path
The points on a curve might represent the path taken by a
cutter, a spray painting nozzle or an adhesive applicator.
crank
rocker
coupler
