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Fig.7. Angular velocity of A and B 

The input of this system is the rotation of the outer ring and the output is the rotation of the blade. The outer ring rotation is related to the theta2 and the rotation of the blade components is related to the theta4. The mechanical advantage of the system is determined by the below equation and all parameters(r_in, w_in, r_out, and w_out) are also described below.

    — (9)

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Image RemovedFig.8. Mechanical advantage versus theta2 angle ( from 200° to 280°)

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Fig.9. Mechanical advantage versus theta2 angle ( from 200° to 270°)

Figure.8. shows the mechanical advantage by changing the theta2. The interesting point is the mechanical advantage drastically increases when theta2 is 277°. Figure 7 shows that w4 is zero when theta2 is 277° and this means that w_out is at this point. Since this makes the denominator of equation 9 zero, the mechanical advantages increase infinitely.

In figure 9, the mechanical advantage gradually increases by increasing the theta2. 

In order to increase the number of blades, the rotation matrix (equation 10 and equation 11) are multiplied to the current data set. Figure 10 and 11 shows the motion of 3-blades Iris mechanism. The ideal theta2 range of motion to fully open and close is determined through the dataset and when theta2 is 230 degrees, the blades are able to cover the inner area.

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Fig.10. 3-blades Iris mechanism: open motion(left) and close motion(right) 

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Fig.11. Simulation from  θ₂=200° to θ₂=230°

The number of blades is increased to 6 and rotation matrices are below. Figure 12 and 13 shows the detail motion of the 6-blades iris mechanism.

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Fig.12. 6-blades Iris mechanism: open motion(left) and closed motion(right) 

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Fig.13. Simulation from  θ₂=200° to θ₂=230°