Main mechanism

The main mechanism consists of the crank and the two links inside the base and the bear's body. This mechanism drives the arm and the head movement.

Figure 1: Motion of the Main Mechanism.

We can consider the mechanism to be divided into two parts:

-The crank and first link within the base.

-The first and second link within the body.

Both links can be modeled as a slotted link with the physical slots being grounded pins on which the links rotate and slide.

First Mechanism

Figure 2: First Part of Main Mechanism.

By solving the loop equation for the first part of the mechanism we get 2 equations to define the rotation θ₃ and length of b₁.

Matlab outputs the following for the angle θ₃ and the length b₁:

Figures 3 & 4: Length b₁ (cm) and Angle θ₃(degrees).

Second Mechanism

The second part of the mechanism depends on the angle and length of link b. The top part of link b extends into the body of the bear and drives the motion of link d. We define the angle of the top part of link b as θ₃₂ and the length that extends into the body as b₂. 

Figure 5: Second Part of Main Mechanism.

In general the angle of b₂ is the same as b₁, the Matlab code, however, outputs the angle as a negative, since it is calculating the vector going down. We can simply use the absolute value of the angle to get θ₃₂. The length b₂ is then defined as the difference between length b and length b₁. The length changes depending on the angle of the crank.

The height, f, and offset, g, of the top slot remain constant so we can find the length of d₁ with simple trigonometry. 

Then we can find theta4 to finish the math for the main mechanism.

Matlab outputs the following plots for d₁ and θ₄:

Figures 6 & 7: Length d₁ (cm) and Angle θ₄(degrees).