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1. 

(a) Sketch all the inversions of a four bar slider-crank mechanism.

(b) Determine the angular velocity of the body shown in the figure below (Triangle ABC is

equilateral).

(c) Label the links and identify lower and higher pairs in the following mechanism. How many

degrees of freedom does it have?

(d)  What type of kinematic pair (lower or higher) is present in the following situations:

I. A sphere constrained to move in a spherical cavity of the same diameter.

II. A sphere constrained to roll on a plane.

(e)  How many degrees of freedom does a round shaft in a coaxial cylinder (as shown below)

have? Assume that the hollow cylinder is fixed.

Figure 2: Note that the link

connecting the two sliders and the

cam follower are separate links.

B C 

Figure 1: Locate the IC and angular

velocity for rigid body ABC. vB is along

vector CB.

 A  

vB 

vA 

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(f)  How many degrees of freedom does the system shown in the figure below have?

(g)  All joints in a planar mechanism with an odd number of links are lower pairs. Can this

mechanism have a degree of freedom equal to 1?

(h) 

A six bar planar mechanism (only has revolute joints) has one degree of freedom. Is it possible for the mechanism to have only binary links with no multiple joints?

2. 

Consider the mechanism shown in Figure 3:

a.  Using Grashof’s criteria, verify that this is a crank-rocker mechanism. Identify the crank

and the rocker links.

Figure 3: Four bar mechanism. L1 = 3,

L2 = 4, L3 = 1 and L4 = 5.

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b. 

Determine the crank angles corresponding to the two extreme positions of the rocker.

What is the time ratio for the mechanism?

c. 

Derive the expression for calculating the transmission angle as a function of the input

crank angle. What are the maximum and minimum values for the transmission angle?

3. For the mechanism shown below,

a) 

Draw any one kinematic inversion. (2)

In the given configuration:

b) 

Determine the position of point P. (2)

c) 

Determine the instantaneous center of link BC. (2)

d) 

Determine the velocities of points C, D, and P; and the angular velocities of links BC and PCD.

(6)

e) 

Determine the acceleration of point P and the angular accelerations of links BC and PCD. (8)

Note: PCD is equilateral. Angular velocity and acceleration

for link AB areω

1 and 1.

 l1 

 l2 

 l3 

 l1 + l2 + l3/2 

 A  

B 

C 

D 

ω1, α1 

P 

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4. The figure below shows the schematic of an aircraft landing gear mechanism in two

configurations: deployed (solid lines) and retracted (dashed lines). Parts 1 and 6 are the hydraulic

actuator and the aircraft body, respectively.

(a) Draw a kinematic diagram of the mechanism. Label the links, and indicate the corresponding parts

on the schematic.

(b) What are the number and type of joints used in this mechanism?

(c) Calculate the number of degrees of freedom for this mechanism.

(d) Determine the kinematic (position, velocity, and acceleration) relationships that describe the

input-outut behavior of the system. Clearly label your diagram, and list any assumptions made.

5. 

For the following – sketch the kinematic diagram, specify the number of links and

joints, and determine the degrees of freedom.

Schematic for an aircraft landing gear

mechanism (Source:

en.wikipedia.org)

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(a) 

Log transporter : wheelslocked with it lifting a log

(b) Throttle

mechanism