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10.3 Kinematic Analysis

10.3 Kinematic Analysis

Ideal Motion:

Figure 1. Hand Calculations of Ideal Motion

 

Motion Profiles of End Effector:

Figure 3. Position Plot
Figure 4. Acceleration Plot
Figure 5. Velocity Plot

Mechanical Advantage for Hand Crank:

image-20250406-031351.png
Figure 6. Mechanical Advantage Calculation
UPDATEDMECHANICALADVANTAGEGRAPH.png
Figure 7. Mechanical Advantage vs. Input Angle Plot

 

nathans work.jpg

Mobility Calculation: (systems and subsystems):

  • Gruebler’s Equation:

    • Number of Links: 7

    • Number of 1 DOF Joints: 8

    • Number of 2 DOF Joints: 0

    • M = 3 ( 7- 1) - 2 (8) -  1 = 1  DOF

    • Note: Because gears are higher pair joints, deduct 1 DOF. 

 

  • Grashof Condition: 

    • Each four-bar is identical

      • L1 = 300 mm, L2 =  50 mm, L3 =  50 mm, L4 =  50 mm

      • S + L = P+ Q

      • This mathematically satisfies the Grashof inequality and suggests that both four-bar links are able to make a full rotation if permitted by the physical limitations of the system.

      • However, the system is physically limited when the links, which exist on the same plane, begin to touch. The system is further limited by the physical presence of the base, meaning that when the end effectors of the four-bar coincide with the base, motion is also constricted. Therefore, the real range of motion for the input link is from ~-45 degrees to ~80 degrees in the final model.

 

Force Analysis: 

mechanism.gif

 

Animation: 

 

 

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