06.3 Kinematics Analysis

Figure 1: Initial Drawing of Mechanism and Linkage Setup (angles are not to scale)

Figure 2: Mean transmission angle; shows mean of 90°(1.5708 radians) at a lenght close to 120 mm

Figure 3: Standard deviation of transmission angle in repeated cuts; shows consistent kinematic behavior with deviations below 3°

Figure 4: Mean cut surface speed in 30 mm vegetables, demonstrating uniformity of speed during major cutting phases

Figure 5: Vertical vs horizontal cut movement; vertical displacement dominates, confirming minimal ‘wasted’ lateral motion

Figure 6: Transmission angle plotted against blade/motor separation.

Figure 7: Blade Velocity plotted against blade/motor separation.

Figure 8: Blade Acceleration plotted against blade/motor separation.

Figure 9: Linkage Animation

Kinematic and Force Analysis

Our prototype employs a four-bar slider-crank mechanism designed to drive a cutting blade vertically through cylindrical vegetables. Initial linkage dimensions were L2 = 30 mm and L3 = 120 mm (see Figure 1: preliminary setup of slider crank), with eccentricity e = 20 mm. To scale up for improved performance, these dimensions were doubled to L2 = 60 mm and L3 = 240 mm, enough to slice through larger vegetables.

Analyzing the transmission angle between L3 and L4, we optimized the linkage so that the transmission angle approaches 90° at both the start and end of the cutting stroke. This maximizes delivered force when initiating and finishing the cut, ensuring penetration through tough outer layers with high efficiency (Figure 6). Throughout the motion, the transmission angle remains greater than 85°, maintaining a favorable force profile.

Velocity and acceleration analyses reveal peak blade velocity at mid-stroke, coinciding with the period of lowest acceleration (minimal wasted effort due to outside movement). Plots of blade velocity and acceleration versus crank/blade separation (Figures 7 and 8) confirm that velocity is highest when force transmission is most efficient.

Motion and Performance Results

Figure 3: Standard deviation of transmission angle in repeated cuts; shows consistent kinematic behavior with deviations below 3°.
Figure 4: Mean cut surface speed in 30 mm vegetables, demonstrating uniformity of speed during major cutting phases.
Figure 5: Vertical vs horizontal cut movement; vertical displacement dominates, confirming minimal ‘wasted’ lateral motion.
Figures 6 – 8: Transmission angle, blade velocity, and acceleration plotted against blade/motor separation. These validate efficient force delivery and stable, smooth cutting motion.

Mobility and Force Calculations

Kinematic mobility analysis gives one degree of freedom controlled by input crank rotation. MATLAB simulations yielded profiles for all major linkage points, indicating peak torque and velocity during the critical cutting phases. Calculated mechanical advantage exceeds 1.6 when the blade contacts the vegetable, providing sufficient force for smooth cutting through typical kitchen vegetables.