Design Process (11)

Design Process (11)

Design Proposal

It was proposed that the basic mechanism of the arm would be a differential bevel gear arrangement. Later, a planetary arrangement was added to power the differential gearset while allowing for full control of the linkage movement.

Operating Principle

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Transmit power from a fixed base (relative to the rest of the arm) to the rest of the arm through a series of gears and linkages.

•Gears centered on the joints of the arm’s linkages can rotate independently of the linkages themselves.

•Motion of powered links (blue) will move unpowered links (green).

 

How it Works - Planetary

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Rotation of the planet gear, powered by a motor, can:

•Rotate the crank arm if the sun is held fixed

•Rotate the sun if the crank arm is held fixed.

One motor can produce 2 different motions, corresponding to the velocity conditions of the arm and sun.

 

How it Works - Bevel

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How are the velocity conditions generated?

•Sun gear shares a shaft with a bevel gear on the other side of the crank arm.

•Bevels want to rotate in the same direction – the 2 powered bevels and base bevel form a simple 3 gear train

•Rotating bevels in the same direction causes the sun gears to freely rotate.

•Rotating bevels in opposite directions locks them up, holding the sun gear stationary.

In Summary

Changing the direction of rotation of the motors relative to each other creates two separate motions.

Each of those motions can be powered by both motors at the same time.

•Compared to delegating one motor per motion, which halves the power available for each motion.

The rotating bevel can be tapped to send its power up to the end of the arm.

Production

All prototypes and the final arm were produced with FDM, as it is a cheap and accessible production method with minimal post processing required, while maintaining acceptable tolerances. The process is also completely automated, allowing us to work on other things while the parts are being made.

Initial Prototype

The bevel gears were designed first to create a simple prototype which tested and confirmed the design and mesh of the bevel gearset. A method of constraining the gears was also established via a center block.

The bevels were created by starting with a set of cones with sides at 45 degrees to the base. From there, the width of the base as well as gear height were identified. Tooth sizes were also determined from geometric analysis. The dimensions of the center block were also determined from this analysis.

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Geometric analysis of bevel gear dimensions
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The initial prototype is on the left. The 3 bevel gears are screwed into a center block. Unfortunately, the wiki doesn’t let you crop images, so the second prototype is in frame.

Second Prototype

The second prototype made several additions to the initial prototype. The center bevel gear was modified to serve as a base for the entire arm assembly. The planetary gearset was also produced, with its fit and function tested. Lastly, a basic four bar linkage system was created to test the arrangement of both gearsets.

Scan_20251213 (2).jpg
Analysis for the required torques and subsequent gear ratios

A load of 1kg at the end of the arm was assumed. From there, the required torque was calculated. A crank length of 50mm was assumed.

The tooth arrangement of the sun and planet were found with the recommendation of a 10 minimum tooth count to avoid undercutting with a 20 degree pressure angle, as per Dudley’s Gear Handbook. From there, the module was found to be 0.5.

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The second prototype is on the right. The planetary gearset wraps around the bevel gearset on the inside. A simple four bar arrangement holds the gears together.

Final Arm

To create an arm capable of reach, the simple four bar made in the second prototype was extended to provide a usable range of motion. Additionally, kinematic analysis determined that the inclusion of a slider joint was necessary to increase the range of motion (presented in kinematic analysis page).

Previous prototypes connected gears using screws, which were incapable of transmitting power. To solve this issue, the final arm uses 1/8” square steel shafts and shaft inserts to transmit rotational power between the planetary and bevel gearsets. The shafts and inserts were taken from the VEX V5 system, as Justin Hung did VEX in high school and had boxes of them sitting around. Shaft collars were also taken from the VEX system as they were a very compact and easy way of constraining lateral shaft movement.

First, modifications were made to mount shafts in the bevel center

prot 2 CS.jpg
Cross section of the second prototype. Coaxial elements are constrained with a simple screw through the assembly.
final CS.jpg
Cross section of the final arm. The addition of shaft collars and bearings in the bevel center for the mounting of shafts can be seen.

Some experimental arrangements were thought of to transmit power to the wrist but were never fully designed and built due to time limitations. Those included spherical gears with monopoles and a more conventional coaxial gear arrangement. The spherical gear was abandoned due to difficulties in generating properly meshing monopoles. The conventional arrangement was designed but never implemented due to requiring changes in the existing arm.

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Design work for the spherical gear.
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Design work for the conventional arrangement

Second, the rear joint between crank and connecting rod was converted into a slider joint

To create a sliding joint, a simple channel was created and a screw inserted. The screw freely slides along the length of the channel, creating a simple, low friction slider with very few parts. The channel sides are at 45 degree angles to the base of the slider to facilitate 3D printing without any supports.

slider profile.png
Frontal profile of the slider. Note the channel shape. The slider base is on the right side

Additional Photos

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CAD model with physical arm. Note the sliding joint between crank (front) and connecting rod.
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CAD model of the arm with the wrist power transmission - conventional arrangement. The extra gears added significant complexity and this version was ultimately not produced.