Mechanism - Clockwork Spindle - Hand Shafts & Gears

The keystone element for Locus Pocus is the clock mechanism. As highlighted in the original conceptual design, several primary elements were needed:

Housing and Face
Hands and Spindle
Motors and Circuit

Conceptual Sketch of Housing and Face — Original Conceptual Design for Primary Components

Conceptual Sketch of Hands and Spindle — Original Conceptual Design for Primary Components

The main constraint on clockwork design was to support multiple clock hands for display. In order to support multiple clock hands, a spindle mechanism is needed with concentric nested shafts, one for each hand. Important design considerations were:

Spindle materials
Drive mechanism for each shaft
How to connect hands on the end of each shaft

Research

I first considered 3D printed standard clocks in order to better understand the potential for a 3D printed design. There are a lot of functional 3D printed clock designs available. One design that I came across seemed to be more straightforward than many others: 3D printed mechanical Clock with Anchor Escapement. I 3D printed the hour, minute, and second gear wheels as a point of reference.

The gears here are of different sizes and have supporting gear elements to transfer second motion to minute motion and to hour motion. But it was very helpful for design to have (1) a visualization of how this is done in a standard clock, and (2) a physical reference that 3D printed spindle / hand shaft elements can work reasonably well.

Standard Clock Hour, Minute, and Second Gear Wheels for Reference

Assembled Standard Clock Hour, Minute, and Second Gear Wheels for Reference

Spindle Design

In considering how to create the spindle components, there seemed to be several different ways previous projects had used create them. Primary considerations are for the construction of the nested shafts for each clock hand and for the shaft gearing (the driven gear). For the shafts, either brass tubing or 3D printing. For the shaft gearing, either 3D printing or pre-made clamp-on gears.

Project	Clock Hand Shaft	Gearing
Weasley Clock	Brass Tubing	COTS Clamping Hub Sized to Each Tube and Aluminum Hub Gear
Where'sLy Clock Project	3D Printed	3D Printed
Magic-Clock	Brass Tubing	3D Printed
The Weasley Clock Project	Brass Tubing	3D Printed

Motor Mounting / Positioning

An important system integration consideration is how to mount the motor in order to couple the motor's driver gear with the clock shaft's driven gear. Mounting of the motors / driver gears needs to account for the spacing between driven gears on the nested shafts. There seemed to be 3 primary approaches to motor mounting.

Mount all the motors at the same level, with fixed framing - in this case, motor shafts need to be long enough and the driver gears need to be height-adjusted on the motor shaft to reach the corresonding driven gear
Mount motors at different levels, with fixed framing - in this case, the motors are mounted at different fixed levels corresponding the the driven gear positions - the levels are set by a fixed design of the framing
Mount motors at different leves, with adjustable framing - in this case, the motors are mounted at different fixed levels corresponding the the driven gear positions - the levels are set by adjustable motor mounts within the framing

Project	Motor Position	Framing
Weasley Clock	Same-Level	Fixed
Where'sLy Clock Project	Multi-Level	Fixed
Magic-Clock	Multi-Level	Adustable
The Weasley Clock Project	Multi-Level	Fixed

Locus Pocus Clockwork Design

For the Locus Pocus project, I selected a spindle design approach that has 3D printed Clock Hand Shafts with 3D printed gearing. For motor mounting, I selected a multi-level, adjustable approach.

In developing Locus Pocus, I used previous approaches as points of reference, but I created all of the designs entirely from scratch. No specific design files or content from other projects were used.

For all of the 3D modeling, I used Autodesk Fusion.

Framing

In order to support a multi-level, adjustable clockwork design, I adopted a platform based approach. The horizontal dimension of the frame consists of cross-shaped structural platforms that space the positions of the vertical supports. The vertical dimension of the frame consists of 1/4 inch diameter threaded rods with an overall length of 6 inches.

Platforms are secured with 1/4 inch nuts on top and bottom. The supporting nuts are tightened in place with secondary jam nuts. The process of fixing a structural platform in place involved first placing the support nuts in approximate position and then placing the platform. Each side (between 2 vertical supports) was then leveled by adjusting the support nuts. Once all sides were level, the jam nuts were tightened against the support nuts to secure them.

In addition to the structural platforms, motor platforms were used to position the motors, using the same process as for the structural

Gear Design

In order to design the clockwork parts, it was first necessary to design the gearing. This was directly connected To select the correct gearing required some research on gear design. There are many references for gear design. Three that I found helpful are:

Create Custom 3D Printable Gears in Fusion 360 | Practical Prints #1
Spur Gears in Fusion 360
Creating a Parametric Gear Model in SolidWorks | Step-by-Step Tutorial - used for theory, not solidworks steps

The primary parameters for a gear include:

Module - size unit for how big or small a gear is.
Pressure angle - gives the direction normal to the tooth profile and can impact gear noise and horsepower. A standard value for this is 20 degrees.
Number of Teeth - how many teeth the gear has
Backlash - tolerance between the gears.
Root Fillet Radius - for fillet at tooth bottom, balances strength and allowance for tooth travel in/out
Pitch Diameter - distance at which gears meet

There are equations that define the relationship between these parameters. For two gears to mesh properly, they need to have the same module.

An important design consideration is also Gear Ratio. A gear ratio is the relationship between # teeth on the driver gear and # teeth on the driven gear. It describes how many times one gear needs to turn for the other gear to turn once fully. The gear ratio can be used to seed up or slow down a driven gear in relation to the motor / driver gear - the corresponding primary tradeoff is torque.

3D modeling software often has gear generators. Typical gear generators, such as accept parameters for Module, # Teeth, Backlash, and Root Fillet Radius, and then determine a pitch diameter radius for the gear. In order to design for a specific distance between 2 gears (with possible differnt # teeth / gear ratio), I used the formulas to compute the necessary modulus for a specific pitch diameter distance and gear ratio.

For Locus Pocus, I considered the motors when designing the gears. Based on earlier experience with the 28BYJ-48, they are comparatively slow (max of ~15 revolutions per minute). I expected this would be a reasonable speed range for the clock hands directly, so I selected a gear ratio of 1:1 (gears with same # teeth / size). For the framing, I wanted the overall clockwork design to be compact, but with enough room to accommodate the size of the motors and adjustable framing parts. I selected a 40mm distance between the centers of the gears, and 32 teeth per gear seemed reasonable. With a 1:1 gear ratio, there was a pitch diameter of 40mm for each gear (~20mm radius). The primary gear parameters were:

Number of Teeth: 32
Gear Ratio: 1:1
Pitch Diameter: 40mm
Module: 1.25
Backlash: 0.15

With the gear parameters set, I created a gear design with the Autodesk Fusion spur gear generator. The spur gear generator is an add-in that comes with Fusion, but it needs to be enabled from the add-ins manager. Since the gearing on the clock hand shaft and on the motor would be the same size (1:1 gear ratio), I created a single primary gear component design as a base component that was copied for use in clock hand shaft design and motor designs.

For the motor designs, a press-fit hole was cut for the dimension of the motor shaft (with a .05mm tolerance).

Gear Modeling in Fusion for Motor Shaft Press-Fit

This gave a very good press-fit on the motor shaft.

For the clock hand shaft designs, a copy of the baseline gear component was added to the bottom of the shaft, just before hollowing the shaft for nesting.

Gear Modeling in Fusion for Bottom of Clock-Hand Shaft

The gearing provided a good fit for the driving motor gear and the driven clock-hand shaft gear.

Overall, the 3D printed gears worked very well. It is important to carefully inspect the prints, as they can be subject to imperfections, such as "elephant foot" - where the first few layers are wider than the rest of the print. I specifically printed without brim or other need for post-processing removal, in order to mimize potential imperfections. Even so, during initial testing, I noticed the whole clock spindle assembly would shift at certain points of rotation. I found some imperfections on one of the motor gears and needed to replace it.

Motor Reference

Because of the many dependencies in the overall clockwork design, it took some iterations to settle on a starting point to anchor the modeling. I decided to begin the overall clockwork design with a reference design for the motor. Initially, I explored the potential for using some existing third-party Fusion 3D models of the 28BYJ-48 motor. However, these came as full 3D models - which presented challenges for extracting the needed dimensions. Moreover, these had been created for different purposes (or slightly different variations of the motor), and the dimensioning was off.

So, I created a reference sketch in Fusion for the key motor dimensions. I used the datasheet for the motor to reference the dimensions, and I confirmed with caliper measurement. Some dimensions of the housing were not specified in the datsheet, and I measured these with calipers.

Stepper Motor Profile Dimensions in Autodesk Fusion

With the stepper motor reference profile set, I projected the needed elements from this component sketch as a basis for modeling other components.

Motor Platform

For the motor platforms and motor gear press-fit, I designed some test fit models to check motor platform setup. This involved testing different offset values for tolerancing on how the motor would fit into the motor platform, and the press-fit dimension for the motor shaft gear.

I tested several iterations for each fit. The main revisions were to reduce the tolerance for tighter press fit on the motor shaft, and to reduce the wire clearance area at the back of the motor.

Structural Platform / Base

With the gearing design and the motor profile in place, I modeled the base structural platform. Based on the gearing design, the distance from the center of the motor shaft to the center of the clockwork needed to be 40mm. In turn, this defined the positioning of the holes for the vertical frame threaded rods.

I designed a half-frame structural platform and initial motor platform to conduct a test fit for the frame design.

Test Fit Design for Structural Platform / Base

3D Printed Pieces for Frame Testing with Motor and Gears

Using the test fit pieces, I assembled a test fit frame with one gear and one motor. I used the manufacturer's basic example code for the motors directly for testing - single revolve forward / reverse. The test fit setup worked fairly well.

Initial Clockwork Test with Structural Frame and Motor Platform

28BYJ-48 Servo Motor Example Rotation Code
//www.elegoo.com
//2018.10.25

/*
  Stepper Motor Control - one revolution

  This program drives a unipolar or bipolar stepper motor.
  The motor is attached to digital pins 8 - 11 of the Arduino.

  The motor should revolve one revolution in one direction, then
  one revolution in the other direction.

*/

#include <Stepper.h>

const int stepsPerRevolution = 2048;  // change this to fit the number of steps per revolution
const int RevolutionsPerMinute = 17;         // Adjustable range of 28BYJ-48 stepper is 0~17 rpm

// initialize the stepper library on pins 8 through 11:
Stepper myStepper(stepsPerRevolution, 8, 10, 9, 11);

void setup() {
  myStepper.setSpeed(RevolutionsPerMinute);
  // initialize the serial port:
  Serial.begin(9600);
}

void loop() {  
  // step one revolution  in one direction:
  Serial.println("clockwise");
  myStepper.step(stepsPerRevolution);
  delay(500);

  // step one revolution in the other direction:
  Serial.println("counterclockwise");
  myStepper.step(-stepsPerRevolution);
  delay(500);
}

Clock-Hand Shafts

With the basic clockwork framing design in shape, I worked on modeling the spindle components, particularly the clock-hand shafts. There were several design considerations for the clock-hand shafts:

Need to be nested, one shaft per hand - centermost (thinnest, longest) to outermost (thickest, shortest)
Need the hand-ends to be spaced to allow attachment of clock hands
Need to connect with the structural platform base, balancing mobility and stability
Need gear bases of the shafts to be spaced to enable alignment with motor gears - allowing for the size of the motors

For connecting with the base, my initial thought was to use a short pin on the base to position the centermost shaft. I designed and 3D printed a test fit with spacers. It was a reasonable fit, but turning the shaft had some wobble.

3D Printed Clock Shaft Testing - V1 - Initial Pin Connection to Base

I tried a similar approach with a thicker, longer pin, as well as additional hand shafts. It was somewhat better, but still not as stable as I would have liked.

3D Printed Clock Shaft Testing - V2 - Larger Pin Connection to Base

3D Printed Clock Shaft Testing - V2 - Additional Shafts

Finally, I tested a central pin that went the entire length of the clock shaft. This seemed to have the best stability while allowing for motion.

3D Printed Clock Shaft Testing - V3 - Pin Through Entire Shaft Assembly

Moving forward with the full-length central pin design, I created a final test fit for a full set of 4 hands with proper hand-end offset spacing. This design had good stability and rotational movement.

3D Printed Clock Shaft Testing - V4 - Pin Through Entire Shaft Assembly with Four Hand Shafts

With the finalized shaft configuration, I incorporated the gearing into the shaft design and 3D printed the penultimate clock hand shafts for testing.

3D Printed Clock Shaft Testing - V5 - Penultimate Clock Hand Shafts With Gearing

In order to test the geared clock hand shafts, I created a final support platform design with the full-length base pin as a hub for the clock hand shafts.

I tested the design first with 2 motors and 2 shafts.

Testing Spindle Design with 2 Motors and 2 Clock Hand Shafts

I then tested a full set of 4 motors and 4 shafts.

Testing Spindle Design with 4 Motors and 4 Clock Hand Shafts

Final Clockwork Revisions

The penultimate clockwork design needed 3 final revisions.

The hand-end offset needed more clearance between the hand-ends
To better support clock hand attachment, the hand-end sides needed to be flattened
While initial testing showed motor / shaft gear alignment to be reasonable, testing with a complementary structural support at the top revealed that the motors were slightly too close. Design of the motor platforms was revised to move the motors 0.7mm further from the center.

Final Revised Clockwork Testing