Final Prototype: Variable Ground Link (VGL) Parallelogram 4-Bar Retractor

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Design

The goals for the redesign were to drastically simplify the linkage, reduce the degrees of freedom to one, reduce the volume and weight, and restore the mechanical advantage of the original finger. To accomplish these goals, we envisioned a simple parallelogram four-bar with two interdependent cranks, as shown below.

Example of graphical synthesis of second prototype linkage

We chose a parallelogram four bar to allow the finger to remain open and vertically oriented throughout the entire retraction motion. The dimensions for this four bar were chosen according to the same reasoning as the first prototype dimensions. The long crank was sized at half the length of the finger, to allow for full retraction when swept through 180 degrees. The short crank was sized to match the actuator link for the existing finger, to allow for seamless integration, and retention of the original mechanical advantage.

To operate the two cranks, we designed a 2-stage gear transmission as shown below. The premise of the transmission is that the driving side, which is connected to the motor, has a full 360 degrees of teeth, and is allowed to rotate completely. The driven side, which is attached to the finger retraction linkage, has two gears with less than 360 degrees of teeth, and limited dependency on each other. The teeth on each driven gear span only the arc that the attached link is designed to rotate, and a pin-slot coupling between the two gears forces them to rotate together for a short part of the rotation. The end result is that the driven gears mesh with the driving gears when they are required to rotate, and become unmeshed when they are required to be grounded.

CAD model of the 2-stage gear transmission and VGL four bar

Motor Tuning

We mounted the finger on a box-like palm, which is where we installed the hand's motor and controls. The earliest design of this palm included a system of spur gears that had three angular velocity step-downs of 5:1, making for a total mechanical advantage of 125:1. The gear at the base of the finger needed to be rotated 280° for the finger to move along a full sweep, so this gave us the number of rotations that the base gear would need to travel (97 rotations.) The motor's spec sheet states that the motor will run at 100 RPM without load, but it had little information about what its velocity would be with load. We tested its capacity experimentally and noted that with this system's (then fingerless) gear system, the  motor's actual speed was far below what was originally expected. We found that, rather than the desired 5 seconds, the finger would need closer to 40 seconds for extension and closure. In future versions of this design, a more powerful motor may be used to obtain the same torque output at the finger. However, for our limited power, we chose to sacrifice torque and grip strength for speed with the prototype, and opted for a redesign with a shorter gear train and smaller mechanical advantage.

Design of palm including the three-stage gear system and accommodations for three fingers.

The second palm design removed the step-downs almost entirely, focusing far more on using the motor's direct drive. We knew what signal to input for the motor to achieve its highest speed, so we started at a small fraction of this, programming the system to move in very small time increments. These results told us how long the finger would need to complete a full sweep at a safe speed, and we hard-programmed this into our code.

Analysis / Verification

Once the design was complete, we simulated the linkage in Matlab to verify the expected motion before manufacture. The plots below describe the physical simulation of the variable four-bar, as well as the X,Y coordinates of the tip of the finger throughout closure, opening, retraction, and extension. The code for this simulation can be found in the Matlab / Arduino Code section.

MATLAB VGL Four Bar Simulation (To Scale)

MATLAB graph showing the finger tip expected path

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