Lecture 3.1 - Synthesis and Analysis of Mechanisms

---

34:10 Synthesis of Mechanisms has different objectives

• Function generation ⇒ Mechanical Calculators/Computers
• Path generation ⇒ Point following a path
• Motion generation ⇒ move something from position 1 to position 2
• Methods of Mechanisms Synthesis
• Graphyical Synthesis of Mechanisms
• Analytical Synthesis of Mechanisms

---

39:30 Extreme positions (in Four-bar mechanism)

Can be used for:

• Positional Analysis by using the given lengths of links, Extreme positions can be found graphically

• Synthesis of Mechanisms to achieve desired motion (e.g. length of a link to achieve a required stroke length)

Why is the difference between the larger angle $\beta$ and the smaller angle $\phi$ equal to $2\delta$?

• $\phi$ needs a $\delta$ to be 180${}^{\circ }$

• $\beta$ is larger than 180${}^{\circ }$ by $\delta$

• So $\phi$ needs another $\delta$ to be as $\beta$

If $\delta =0$, $\phi =\beta$, return = go Two extreme positions coincide on each other

Note: Quick-return ratio can be used for Positional Analysis (see problem 1.7 in Sheet 1) and Synthesis of Mechanisms (e.g. Rocker-output, quick return) as well

---

45:55 Synthesis of four-bar mechanism

---

48:56 Rocker-output, equal time for go and return - Angular Displacement - Required: Angular Displacement

---

54:41 Rocker-output, equal time for go and return - Complex motion - Required: Complex motion

• General Plane Motion ⇒ Rotational Motion about a fixed point
• Finding center of an arc
• B is lower pair

To make the motion happen in equal time: Note: blue rectangle = one rigid link

---

01:03:54 Rocker-output, quick return

How to calculate $\delta$?

How was the radius of crank obtained in this way?

Crank + Coupler = OB1 Coupler - Crank = OB2

How to draw rocker?

• Draw a line with angle $\delta$ between the locus of hinge of the crank (O)
• Draw a line that is parallel to that line and intersects with B2

---