Kinematic Analysis of Iris Mechanism

Fig.2. 6 blades Iris mechanism kinematic structure.(concept design)

Figure2. shows the kinematic structure of the Iris mechanism. Blue circle line is the outer actuation ring, black lines are the links, and O₂ is the center of the rotation. Since the blade is connected to the R_BO4link, we can decide the shape and angle of the blade after finishing the kinematic analysis of the linkage mechanism.

Fig.3. kinematic for 1-blade(left) and four-bar linkage system of the one blade(right)

In order to do the kinematic analysis of the Iris mechanism, I focused on only one blade because other blades have the same kinematic structure and characteristics. If we draw imaginary links such as R_O2A and R_O2O4, we can know that this is the four-bar mechanism which is described as Fig.3. Based on the concept design which is Fig.2., design specifications such as length of links(a,b,c, and d) and fixed joint angle(theta2) are determined and described below.

In the four-bar mechanism system, the closed-loop equation for the position analysis is

Where theta3 and theta4 are unknown variables of the mechanism and theta2 joint variable is rotated by the outer actuation ring. Theta 3 and theta4 are determined by the other given elements using the above closed-loop equations(eq.3. and eq.4.) and the below plot shows the x and y position of the joint B by changing the theta2.

Fig.4. movable area

Fig.5. linkage position at θ₂=190°(left) and θ₂=200°(right)

Figure 4 shows the reasonable theta 2 angles to move the blades. As shown in Fig.5, the linkage position is significantly changed when theta2 is around 195°.

In addition, since y position of point B is decreased after theta2 is 280°, the expected range of motion of the theta 2 is from 200° to 280°. The below figure 6 shows the motion of the one blade as theta2 rotates in the expected range of motion.

Fig6. Simulation from θ₂=200° to θ₂=280°

By differentiating equation 1, the unknown velocity parameters (w3 and w4) can be determined.

Since point A is the fixed joint, theta 1 is constant, which means that w1 is zero. The w2 is arbitrary given as 1 rad/sec in order to find the w3 and w4. the angular velocity of A and B by changing the theta2 is shown in Fig.7.

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)

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

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(w_out) is zero when theta2 is 277° and this means that this is the toggle 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.

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

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.

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

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