03 - Kinematic Analysis

The team decided to strive and design a mechanism that would run with a single input to drive both the linear motion of the whetstone and the rotation of the knife. The general design was mocked up in MotionGen, as seen in the gif below, that consists of a single rotational input link that is connected to a prismatic slider-crank for the whetstone and a four-bar mechanism for the knife. This will allow for the slider-crank and the four-bar to be on the same cycle, rotating the knife and moving the whetstone at the same frequency, just at different velocities and positions.

As stated above, the system can be broken into two systems connected by the input link. For the slider-crank, the design of the ternary prismatic joint is meant to have the shorter length (labeled L2) be significantly larger than the input length (labeled R) so that the system oscillates during a full rotation of the input link. The longer length of the prismatic joint that connects to the linear slide (labeled L3) needs to be significantly longer than L2 in order to act as a gear ratio that amplifies the arc length of the oscillation on the joint, since the whetstone will need to move the length of the knife in half a revolution of the driving motor. For the four-bar, the length of the driving bar (labeled L6) must be significantly larger than R for the same reason as L2, although L6 will end up being giving a much smaller arc length of rotation than the whetstone since the rotation of the knife does not need to be nearly as great as the linear range of the whetstone.

Kinematic Analysis

The kinematic analysis was done via MatLab to create plots of both the position and the velocity of each system in the design. The purpose of the kinematic analysis is to determine how changing the lengths of the various links in the system can create a system that minimizes the variance in how much each part of the knife is being sharpened, while still creating something that is functional. The initial plots shown below are with arbitrary lengths (measured from the MotionGen simulation) and an arbitrary input angular velocity of 360 degrees/second. This was just to give the team a baseline of how the system operates and how changing each length impacts the total motion of the mechanism.

                             Whetstone Slider-Crank

a = 1.00;            % crank length [m] or suitable unit like [mm]

b = 7.25;            % coupler length [m]

c0 = 3.5;           % rocker length [m]

d = 9;            % ground length [m]

p = 7.25;            % distance to coupler point from point A [m]

delta3 = 0;        % angle from coupler to coupler point line [degrees]

omega2 = 2*pi;         % crank angular velocity [rad/s]

>> Need to multiply velocity graph all by 11.5/3.5 to account for actual design:

                         Knife Four-Bar

a = 1.00;            % crank length [m] or suitable unit like [mm]

b = 17.5;            % coupler length [m] 

c0 = 5.5;           % rocker length [m]

d = 19;            % ground length [m] 

p = 17.5;            % distance to coupler point from point A [m]

delta3 = 0;        % angle from coupler to coupler point line [degrees]

omega2 = 2*pi;         % crank angular velocity [rad/s]

Further kinematic analysis will be performed as the team continues to determine the desired operation speed of the mechanism, especially since, as seen in the slider-crank analysis, there is a very large amplitude in the speed profile, which could cause uneven sharpening on the knife since the middle section of the knife is in less contact with the knife on the four-bar that rotates with a much smaller speed amplitude.

Prototyping Reflection

Our current prototype acts as a proof of concept for the style of mechanism that we believe will give us the motion profile we desire. Our future iterations must include several major modifications, including a device to grip onto the knife, a spring loaded mechanism to hold the whetstone, and a motor attached to the input crank. We must also modify the location of several of the joints in order to create enough space for the knife and whetstone. Finally, our current prototype does not quite give us our desired motion profile. The knife rotates too much at the beginning of its movement which does not allow enough time for the whetstone to sharpen it at that orientation. We will have to experiment with the lengths of the linkages in order to get the movement we want. 

BOM