10.1 Project Proposal - Matcha Whisk
Introduction:
Matcha, a finely ground powder made from specially grown green tea leaves, has been consumed for centuries and holds deep cultural significance in Japan. In recent years, matcha has rapidly gained popularity in the United States due to its distinctive flavor and widely recognized health benefits.
Because matcha is sold as a fine powder, it must be whisked into hot water before it can be consumed on its own or combined with milk to create beverages such as matcha lattes. Traditional preparation requires the use of a chasen, a bamboo tea whisk, along with specific whisking techniques that help properly dissolve the powder and produce a smooth, frothy texture. For many people unfamiliar with these tools and techniques, the preparation process can feel inconvenient or intimidating, which can make it less appealing for others to prepare matcha at home.
However, the preparation process plays an important role in achieving the desired taste and texture of the drink. Developing a mechanism that can assist or automate the whisking process could simplify matcha preparation while still preserving drink quality. This would make matcha more accessible to a broader audience and allow more people to easily incorporate it into their daily routines.
Figure 1: Matcha Preparation Process
Problem Statement:
Preparing matcha requires a specific whisking motion that is difficult to replicate consistently without practice. Traditionally, the chasen is moved in a rapid zigzag pattern across the bowl, creating repeated back and forth stokes in the horizontal plane while keeping the whisk at a nearly constant height above the bottom of the bowl. This motion helps propertly mix the liquid to create the characteristic light foam while also dispersing the matcha power so there are no clumps found.
The zig-zag pattern involved coordinated movement in the two perpendicular horizontal directions, with frequent and rapid changes in direction. In addition, the whisk typically moves faster in one direction than the other, which creates a path similar to that of a Lissajous Pattern rather than a simple back and forth or circular motion. Because of this difference in motion between the axes, the whisking pattern can’t be generated by a single rotating joint or other simple one degree of freedom mechanism. At the same time, the vertical position of the whisk must remain tightly controlled so that the whisk stays close to the bowl in order to mix the liquid without scrapping the surface of the bowl. Producing this coordinated two-axis motion while also maintaining a fixed vertical position will require multiple degrees of freedom.
Figure 2: Matcha Whisking (Zig-Zag) Motion
Mechanism:
The complete matcha whisking system can be divided into fundamentally two sub-mechanisms that work together in order to generate the required two-axis whisking motion. Both sub-mechanisms are slider-crank mechanisms that will convert a 360° rotary input into a linear motion. The first slider -crank drives a vertical bar horizontally along a set of rails, controlling the left to right motion of the whisk. The second slider moves within the vertical slider bar and controls the up and down position of the whisk. By nesting one slider inside the output of another, the two independent linear motions combine at a single output point, which is at the whisk’s tip, in order to trace a zig-zag path that is required for effective matcha whisking.
Rather than utilizing two independent motors, the entire system will be powered by a single motor. A gear train will distribute the rotary input to both the slider-crank mechanisms so that they would be able to operate simultaneously without any offset delay. The current gear configuration will be arranged to have a 1:3 ratio between both a input crank links, meaning that one axis will complete three revolutions for every one revolutions of the other. The difference in frequency will produce the desired zig-zag whisking pattern instead of a simple circular or elliptical pattern.
It should be noted that alternative mechanisms such as a four-bar linkage or cam-follower were considered, but the slider-crank was selected for its mechanical simplicity, compact form factor, and ability to produce a well-defined linear stroke length that can be easily tuned by adjusting the crank radius.
Proposed Scope:
Our prosed deliverable is a fully functional matcha whisking device that is capable of preparing a perfect cup of matcha by replicating the traditional zig-zag whisking motion. The mechanism will be driven by a single motor and will generate the required two-axis zig-zag trajectory through a nested slider-crank system connected by a gear train. Below are the development process steps to construct the matcha whisking device:
Finalize the gear train configuration to achieve the 1:3 crank frequency ratio between the two slider-crank mechanisms by determining the gear tooth counts and arrangement needed.
Design and analyze each slider-crank mechanism individually. This would include establishing the crank radii and geometry to produce the desired stroke lengths in both axes while remaining within the constraints of the bowl’s dimensions.
3D Print/Laser-Cut Parts and assemble the mechanism.
Attach the chasen to the output slider and test in a bowl with matcha or a matcha equivalent replacement. The success criteria for this part would include the prepared matcha produces a visible froth and containing no clumps in the mixture.
Additional Analysis that will be needed before the final fabrication:
Verify Gruebler and Grashof Conditions by confirming the correct numbers of degrees of freedom and that both cranks achieve a fill 360° rotation under all configurations.
Complete Position and Velocity Analysis by analytically deriving the whisk tip trajectory and verify that it matches the desired zig-zag pattern before any of the part are printed/laser-cut.
Optimize Gear Train Ratio by verifying through analysis that the 1:3 ratio produces effective whisking. If the testing reveals that there is poor froth or incomplete power dispersions then we will have to adjust the gear tooth counts or ratio accordantly.
If additional time were available, future work could include developing an adjustable mount to accommodate different bowl sizes and experimenting with alternative gear ratios to optimize whisking performance for different matcha consistencies.
Preliminary Design:
For our proposed mechanism we will have two slider-crank mechanisms nested within one another, where the output of the first serves as the moved frame for the second. Each sub-mechanism is in charge of driving the motion along one axis and together both of the sub-mechanisms work together to produce the two-dimensional zig-zag trajectory required for the effect matcha whisking.
The first slider-crank mechanism converts its 360° rotary input into horizontal motion. The crank rotates about a grounded pivot, driving a coupler link that pushes a vertical slotted bar left and right along a set of fixed horizontal linear rails. This slotted bar acts as a the moving frame for the second sub-mechanism and contains its horizontal position entirely.
The second slider-crank mechanism is nest inside the slotted bar of the first one. Its crank rotates about a grounded pivot and drives a coupler link that moves a slider up and down within the slotted bar. The end of this coupler link is connected to the whisk via a revolute joint, which serves as the final output point of the full mechanism. Note that the motionGen diagram provided below shows both coupler links connected, which was a limitation of the software. In the physical build, the two coupler links will not be connected to one another, allowing for both cranks to achieve a full 360° rotation independently. Although the MotionGen model still produces a motion capable of preparing matcha, the final physical design will allow for a larger zigzag trajectory to improve whisking performance.
To better visualize how the full mechanism will behave in the real-life build, an animation was created to simulate the nested slider-crank system in motion. This simulation shows both cranks operating simultaneously at the 1:3 frequency ratio, the slotted bar sliding horizontally along the rails and the resulting zig-zag path traced by the whisk tip. This image was generated in order to provide a clearer representation of the physical build in addition to the motionGen diagram.
The two mechanisms are powered by a single motor through a gear train that delivers a 1:3 angular velocity ratio between the two cranks. The first crank that is responsible for the horizontal motion will rotates at one-third the speed of the second crank, which drives the vertical motion. This means the whisk completes three vertical strokes for everyone horizontal stroke producing the asymmetric zigzag path characteristic of traditional matcha whisking. The current gear tooth design includes a 12-tooth driving gear with a 36-tooth driven gear in order to achieve this ratio.
Gruebler's Calculations:
M = 3(L-1) - 2J1 - J2
M - Mobility of the system (Degrees of freedom)
L - Number of links in the mechanism
J1 - Number of 1 DOF joints
J2 - Number of 2 DOF joints
Proposed design:
L = 7 | J1 = 8 | J2 = 0
M = 3(7-1) - 2(8) - 0 = 2
This gives us 2 degrees of freedom, which represents the motion in both the X and Y directions, respectively. However, it should be noted that since the two inputs are kinematically constrains to one another since both cranks are going to be powered by a single motor through a gear train at a fixed 1:3 ratio this will effectively reduce our system to 1 degrees of freedom in practice.
Grashof's Law:
Grashof’s Law is used to determine whether a linkage can achieve a full continuous rotation.
Grashof Equation: S + L <,=,> P + Q
S: Shortest Link | P: First Remaining Link
L: Longest Link | Q: Second Remaining Link
For our mechanism, the stroke of the whisk in each direction is determined entirely by the crank radius of each slider-crank sub-mechanism. With a target bowl diameter of around 5.3 inches, we propose a crank radius of 0.75 inches for both sub-mechanisms, which would produce a total stroke of 3 inches of motion in each axis. The coupler link is chosen to be 2 inches for both slider-crank mechanisms. Since the coupler link is longer than the crank radius (2 inches > 0.75 inches), the linkage avoids toggle positions and allows the crank to rotate continuously through a full 360° rotation. It should be noted that these values will change during the prototyping phase in order to find the optimal link lengths to properly mix the matcha power sufficiently.
Additional Brainstorming Idea:
This configuration is almost the same as Design #1 that was chosen for the final build, but the second slider crank that creates up and down motion in the slotted link is replaced by a cam-follower. A slider-crank is still used to generate horizontal movement along the two grounded linear rails. The whisk is attached to the end of the follower and will be to one side of the linear rails instead of in the center as in the previous design.
Instead of a slotted link moving along the rails, this configuration will have a wider, solid link (bright red rectangle in the figure above). The cam and follower will be mounted on this central link along with the servo used to power the cam. The cam will likely have some sort of oval shape so as to get perpendicular motion relative to the linear rails. If circular, the follower would never move relative to its initial position. As for the follower, it will likely be a roller follower to minimize friction in the mechanism overall.
Since we cannot utilize gravity to keep the follower attached to the cam, some sort of spring loaded joint will have to be created. This is future work if this design is the one that we go with.
Some images providing more detail about cam-follower joints is below:
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A very preliminary simulation of the mechanism was created in MATLAB to understand the path of the whisk end effector. The results are seen below:
The most valuable information achieved with this simulation was that the frequency of the cam-follower motion much be much higher than that of the slider crank in order to achieve a zig-zag pattern of sorts. The exact difference in frequencies, as well as exact link lengths will be determined in the future if this idea moves forward.