Team 8: Kinematic Analysis & Synthesis

Mobility Calculation (DOF)

Using Gruebler’s equation of mobility, M = 3(L-1)-2(J1)-J2, we can calculate, M, the degrees of freedom of our stamping mechanism, with L number of links, J1 number of full joints, J2 number of half joints. With the total number of links being 6 and the total number of joints being 7, M = 3(6-1)-2(7)-0. The degrees of freedom are calculated to be 1.

Position and Velocity Analysis

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Figure 1. Position and Velocity Calculations with Respect to 𝜽2 and ω2

Figure 2. Input Angular Position vs. Output Angular Positions (Stamp Output: ⍺4)

Figure 3. Input Angular Position vs. Output Angular Velocities (Stamp Output: ω⍺4)

It is important to note that when calculating the angular positions of each of the 6 linkages, that ⍺2 is equivalent to 𝜽4 as shown in Figure 1. Therefore, the angular position curve of 𝜽4 matches that of ⍺2 in Figure 2 since they are both the angular positions of Linkage C. Using this relation, we are able to split the 6-bar linkage into two 4-bar linkages in order to solve for the respective angular positions and velocities. It can also be seen that the respective angular velocities of 𝜽4 and ⍺2 are equivalent curves because they are essentially referring to the same linkage, as shown in Figure 3. Furthermore, the angular velocity stays relatively constant throughout the rotation of Linkage A. Because of these kinematics, the stamping Linkage H has a stable and consistent output in pressing ink into our desired medium.

Linkage Animation: