Synthesis
It depends on………….
(i) What type of mechanism will be suitable?
Linkage/ Cam/Gears/Pneumatic cylinders/Other/Combination of them.
(ii) How many links/what configuration is desirable?
Type of Synthesis
(i) Quantitative Synthesis: Used when a mathematical technique exists to directly create a solution. (Only for certain classes of problems)
(ii) Qualitative Synthesis:
a. Used when no mathematical technique exists.
b. Sometimes requires ‘design by successive analysis’
1. Assume a possible solution
2. Analyze it to determine suitability
3. Revise solution based on insights gained in the analysis
Linkage Three Types
(i) Function Generation: Correlation of an input motion with an output motion in a mechanism. Output motion is a defined mathematical function of the input motion, e.g., x = r cos (q).
(ii) Path Generation: Control of a point in the plane such that it follows some prescribed path. Output motion is a defined path along a set of x,y points.
Film Advance Mechanism: This is accomplished with four bars, wherein a point on the coupler traces the desired path
Note that no attempt is made in path generation to control the orientation of the link that contains the point of interest
(iii) Motion Generation: Control of a line in the plane such that it follows some prescribed path. Output motion is a set of positions of a line defined as x, y, q successive locations.
Three Positions of a Line
Here orientation of the link containing the line is important.
Path generation is a subset of motion generation
e.g.: control of the bucket in a bulldozer. Bucket must assume set of positions to dig, pick up and dump the excavated earth
Dimensional Synthesis
Determines the principal dimensions (pivot to pivot distances, angle between bell crank levers, cam-contour dimensions and cam-follower diameters, eccentricities, gear ratios) and the starting position of the mechanism to perform the required task.
a. Applicable to all three modalities: path, motion, or function synthesis.
b. Can be done either graphically or analytically.
c. One method can be used to check the other.
Two Position Synthesis
(i) Rocker output (pure rotation): Suitable when Grashoff crank-rocker is desired, a case of function generation in which the output function is defined as two discrete angular positions of the rocker
(ii) Coupler output (complex rotation): Case of motion generation in which two positions of a line in the plane are defined as the output. Frequently lead to triple rocker
Time Ratio in Quick Return Mechanism
A measure of the quick return action of a mechanism is the time ratio, Q which is defined as follows
An imbalance angle b is a property that relates the geometry of a specific linkage to the timing of the stroke. This angle can be related to the time ratio, Q.
Total cycle time for the mechanism is 
tcycle = time of slower stroke + time of faster stroke
For mechanisms that are driven with a constant speed rotational actuator, the required crank speed, wcrank is related to the cycle time is as follows
In line Slider Crank Mechanism
The stroke is defined as the linear distance that the sliding link exhibits between the extreme positions
Because the motion of the crank (L2) and connection arm (L3) is symmetric about the sliding axis, the crank angle required to execute a forward stroke is the same as that for the return stroke .For this reason, the inline slider-crank mechanism produces balanced motion
Assuming that the crank is driven with a constant velocity sources, an an electric motor, the time consumed during a forward stroke is equivalent to the time for the return stroke
Design of an inline slider crank mechanism involves determining the appropriate length of the two links, L2 and L3 to achieve the desired stroke. As seen from the figure, the stroke of the inline slider crank mechanism is twice the length of the crank
Length of the connecting arm L3 does not affect the stroke of an in-line slider-crank mechanism. However a shorter connecting arm yields greater acceleration values
Fig illustrates the effect of connecting arm length and offset distance (if any) on the max acceleration of the sliding link.
Offset Slider-Crank Mechanism
The offset distance L1 is the distance between the crank pivot and the sliding axis
With the presence of an offset, the motion of the crank and connecting arm is no longer symmetric about the sliding axis. Therefore, the crank angle required to execute the forward stroke is different from the crank angle required for the return stroke
An offset slider-crank mechanism provides a quick return when the slower working stroke is needed.
It should be noted that A, C1 and C2 are not collinear. Thus the stroke of an offset slider crank mechanism is always greater than twice the crank length
As the offset distance increases, the stroke also becomes larger
Feasible range of offset distance can be written as L1<L3-L2
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