Question

Rods of varying length (± 10%) travel one at a time in the direction of their longest axis on a conveyor belt. A mechanical arm pushes rods that are within specification (± 5%) off the belt to one side. A second arm pushes rods that are too long to the other side. Rods that are too short remain on the belt. Use three light barriers (light source + photocell) as sensors, and design the combinational circuits that activate the two arms.

Answer 1

There are two arms ARM₁ and ARM₂, and there are three Light barriers L₁, L₂ and L₃.

ARM₁ and ARM₂ are activated when they recieve 1 and they don't activate when they receive 0.

ARM₁ pushes the rods in specification to one side and ARM₂ pushes the rods that are too long to another side.

Light barriers L₁, L₂ and L₃ are actually in 1 state ie. they are unblocked. When they are blocked they come to 0 state.

The Light barrier L₁ is blocked when the rod reaches that point, at this moment the state of other light barriers are checked to determine whether the rod is too long or is under specified dimensions.

Now, the light barrier L₂ is placed at a distance of L-5% and the light barrier L₃ is placed at a distance of L+5%+. Here this small distance has been put so that, when the rod reaches L₁ , if the rod is under specified dimensions the light barriers L₁ and L₂ would both be in 0 state but due to this small distance, L₃ will still be in 1 state. If the rod length is more than the specified dimensions all the light barriers will be in 0 state and we can activate the ARM₂. If the rod length is at correct dimensions ie. L₁ and L₂ are in 0 state, and L₃ is in 1 state, then we can activate ARM₁. In the next case when only L₁ is activated it means that the rod length is less than L-5%. So, no ARM is activated. Based on this data we can construct the combinational circuits required to activate the two arms.

The logic table is as given below,

L1	L2	L3	ARM1	ARM2
0	0	0	0	0
0	0	1	1	0
0	1	0	0	0
0	1	1	0	0
1	0	0	0	0
1	0	1	0	0
1	1	0	0	0
1	1	1	0	1

For Finding the Logical expression, we will use the Sum of Products method in which we have to add the minterms having the output 1.

Hence for ARM₁ we can write the logical expression as,

and for ARM₂ we can write the logical expression as,

So this is the required combinational circuit for each of the Arms.