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  1. a) A client wishes to change his conveyor belt. He used to have a 20cm diameter tail pulley equipped with an absolute encoder of 12 bits. The new conveyor will come with a 25cm diameter tail pulley. The client asks you to choose the new encoder to keep the same belt linear position resolution.

Figure Q1- Conveyor belt


  1. Compute the belt linear position resolution with the old pulley and old encoder. ii. Compute the angular resolution required for the new conveyor belt.
  • Calculate the number of impulses per revolution an incremental encoder would require to reach this angular resolution
  1. Calculate the minimum number of bits needed to achieve the same resolution and state how many tracks a new absolute encoder requires.

[8 marks]

  1. b) The conveyor belt is used to transport 50cmx50cmx50cm cardboard boxes. The client would like the conveyor to transport 20 boxes per minutes with a conveyor speed of 1.2m/s.
  2. Compute the maximum distance between 2 cardboards to respect the client specifications. ii. Propose a sensor that could detect when a cardboard box is passing on the conveyor belt.

iii. Calculate the minimum distance between two boxes if the time response of the sensor is 200ms. iv. With this minimum distance, how many boxes per minute the conveyor could transport with the same speed of 1.2m/s?

[8 marks]


  1. c) Explain the differences between backlighting and top lighting in machine vision, and mention two examples where each could be used in an industrial process.

[4 marks]





Q2. Two sensors A and B are used to count the number of people in a shop. We would like to design the sequential logic circuit that would lock the door entrance (L) when the limit of 3 people is reached in the shop using JK flip flops. The sensor A is placed at the entrance of the shop and the sensor B is placed at the exit of the shop. We assume that A and B cannot be activated together. If A is triggered when 3 people are in the shop, or if no one is in the shop and B is activated, the system should remain in the same state but an error signal (E) should be activated.


  1. What kind of sensors could be used for A and B?            [3 marks]


  1. Draw the sequential state diagram for the required design, clearly stating the transition conditions and output values, using the Mealy model. (Hint: the state numbers could be equal to the number of people in the

shop)                                                                                               [5 marks]

  1. Make a truth table containing the next state and output.

[3 marks] d) Make a table showing the J and K input values required to implement this machine using JK Flip-flops (this can be done by expanding the table in c).

[3 marks]

  1. e) Using Karnaugh maps, give the logic equations of each input of the JK flip-flops and for the two outputs L and E.

[6 marks]



Q3. The station shown in Figure Q3 is a sorting station for parcels. The following sequence describes the sorting process:

  • The start button should be pressed to start the process
  • The conveyor A is used to transport the parcels to the lifting platform.
  • When the proximity sensor (P) detects that a parcel reaches the lifting platform, the conveyor A (CA) is stopped and the cylinder 1 is extended to lift the platform.
  • Once the lifting platform is up the optical sensor (H) is used to measure the height of the parcel. If the parcel is taller than 10 cm, the sensor H is activated. If the parcel is smaller than 10 cm, the sensor H is off.
  • If the parcel is taller than 10cm, it is sent on the conveyor B using the cylinder 2.
  • If the parcel is small, it is sent to the conveyor C belt using the single acting cylinder 3.
  • The system comes back to its initial position (all cylinder retracted)
  • The sorting process should repeat.
  • The stop button can be used at any time to stop the process

For safety reason, cylinder 2 should be extended only if cylinder 3 is retracted and cylinder 1 extended. Similarly, cylinder 3 should be extended only if cylinder 2 is retracted and cylinder 1 extended. Also, cylinder 1 should not start its extension if cylinder 2 or cylinder 3 are not retracted. Finally, the conveyor should not be running if cylinder 1 is not retracted.


/Question continued on next page

To move up and down the cylinder 1, two pneumatic 3/2 way single solenoid directional control valves (DCVs) with spring return are used (C1+ for extending and C1- for retracting).

The cylinder 2 is connected to a 5/2  way single solenoid DCV with pneumatic return (C2).

Cylinder 3 is connected to a 3/2 way single solenoid DCV with pneumatic return (C3).

In addition, one way flow control valves are used to limit the air flow in the cylinder and smooth the motion.

Two sensors magnetic sensors are used to detect when the cylinder 1 is retracted (a0) or extended (a1). Cylinder 2 and cylinder 3 are equipped with only one magnetic sensor each to detect when they are retracted (b for cylinder 2 and c for cylinder 3). Therefore, a timer is used to leave enough time for the cylinders to extend (2s for both).

After the timer ends, cylinder 1 and cylinder 2 or 3 retracts. Once cylinder 1 is fully retracted, the conveyor A is switched on again and the sequence can start again.


  1. a) Draw the pneumatic diagram of the system.

[8 marks] b) Design a ladder program for a PLC to automate the sequence previously described (no need to control conveyor B and C).

[12 marks]




  1. Consider the three-link planar arm shown in Figure Q4 with links’ lengths: 𝐿1 = 800mm, 𝐿2 = 250mm and 𝐿3 = 120mm, and the cartesian coordinates of the gripper are 𝑥 = 825mm and 𝑦 = 135mm (with respect to 𝑅0 =

(𝑂0, 𝒙𝟎, 𝒚𝟎, 𝒛𝟎)) and the gripper is at an angle 𝛼 =52° measured anticlockwise from the 𝒙𝟎 axis.


  1. Use the inverse kinematics transformation to determine the joint angles 𝜃1, 𝜃2 and 𝜃3.
  2. State what type of joints are used in this robot, give the robot architecture.
  • Following the Denavit-Hartenberg notation, make a table that shows the DH parameters of the planar arm.

[12 marks]


  1. A 3 Degrees of Freedom robot is described by the following DenavitHartenberg table.

Table 1 – DH table

𝒊 𝜶𝒊 𝒂𝒊 𝒅𝒊 𝜽𝒊
1 0 0 𝒅𝟏 𝟎
2 𝝅



𝒂𝟐 = 𝟎. 𝟒 0 𝜽𝟐
3 𝝅


𝒂𝟑 = 𝟎. 𝟐 0 𝜽𝟑



  1. Give the transformation matrices between each link. ii. Compute the position of the end effector for the following joint coordinate vector:

𝑑1 = 0.6

𝑞 = ( 𝜃2 = π )

𝜃3 = 0

[8 marks]


End of paper