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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.
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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.
Fig5Fig6. simulation Simulation from θ2=200° to θ2=280°(toggle position)
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
