Curtate Cycloid
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Hi Mr Jeph_s22, FusionCarDrivers,
Preamble context:
I briefly looked at the post out of curiosity and found some innovative suggestions, though they have not been fully "consumed".
Please take my first thoughts on what I found there... lightly...
Yes, I also spent a lot of time in school on geometry lessons, catching flies, both those resting, chewing on my sandwich, and others in extra-vigorous flights… nevertheless, I was so skillful (at catching them) that I still had time to listen to a teacher and look at the blackboard.
And yes, I understand that converting geometry concepts to the Fusion paradigm isn't always easy, especially for new adepts, who deserve thus an excuse ticket.
On the serious matter now…
First, I want to clarify my understanding of the basic design intention.
- Bin is supported by circular arc elements
- Rolls on the straight track
- Arcs have equidistant teeth
- The track has cutouts at distances matching the arc spacing of the teeth
- Teeth and the corresponding cutouts are to add additional mechanical rolling constraint
- The pin-slot feature adds the motion/roll limits to the design
- I will not discuss the validity/quality/workability/… of the presented ‘garbage hopper’ concept; it is as it is.
How to tackle the issue: Geometry first.
- The circle (arc) rolling distance is linearly π-derived from its rotation angle.
- It should be obvious unless someone lacks fly-catching skills.
- The shape of the motion-limit slot is a little bit trickier. The point inside a circle rolling on a straight line traces a trochoidal curve, specifically a curtate cycloid. The mathematical definition is simple, and the design clearly shows all necessary input arguments.
Move to the Fusion next.
- Point 1. From the previous cluster, it can be easily implemented as a rolling motion link. Check the joint <_Pin_Slot_Rolling> and related motion link <ML_Rolling>
- Details are in the file for investigation
- Obviously, <Constraint 12 tangent> must be suppressed/deleted as redundant
- Anyway, such constraints are expensive and should be used in circumstances when the classical motion tools are insufficient (e.g., for non-circular objects)
- The design contains some other < Constraints>. The previous point applies there. Preferably use <Joint Origins> followed by the classical joints.
- How to implement a "curtate cycloid" curve for the motion-limit-slot. Well, it depends upon "flies catching skill"
- Develop the slot curve mathematically
- Use sketch drawing to find out a few points along the motion range
- As you will see in the demo file provided, the slot can be cut automatically using Boolean operations, following the system's kinematics. Unfortunately, the functionality you see in the video isn't available in standard Fusion (as far as I know).
- Still, you can replicate (c.) point in the manual fashion. Refer to the supplementary links provided.
- As a last resort, capture a screen and find the point organoleptically.
- A cartoon mockup model could also nicely clarify this and many other issues.
I am attaching the modified/simplified design, just to make the system workable.
Perhaps, to avoid future problems while refining the concepts, an additional design methodology audit of your design/concept could benefit the final design at this early stage.
As I indicated in the "introductory" post. Your "pin" problems are only a minuscule part of the global struggle in many people's lives, sorry to say… it is insignificant. Some would even say marginal.
The kinematics you implemented (which play a role in your system) drain many car drivers' nerves daily, particularly those who are ɥappily married… well, because most of them aren't aware of the mathematical philosophy behind it and, well, because they lack fly-catching skill.
How do such kinematics and their respective mathematical formulations affect millions?
Hopefully, the following visuals don't need further explanation…???
Mentioning "mathematical formula" brings me back to the issue I already raised on the forum. The dialogue input box doesn't let one draw such formulas concisely and in an eye-pleasing way. Hopefully this repeated mention reaches the TF360 decision-makers, slowly but surely, far away in never-mind land.
Attached Files:
Hopper Demo_MT.f3d F3D (0.7MB) https://a360.co/4dDCSmH
Hopper_mono.mp4 4K_mono (0.9MB) https://a360.co/4B8kCfl
Hopper_mono.png 4K_mono (0.6MB) https://a360.co/4s4b1BX
CurtateCycloid_mono.mp4 4K_mono (2.1MB) https://a360.co/3WuoC9S
CurtateCycloid_mono.png 4K_mono (0.3MB) https://a360.co/4zaOOVT
Supplementary links:
https://forums.autodesk.com/t5/fusion-design-validate-document/body-sweep/m-p/12771763
Regards
MichaelT
P.S.
The slider values displayed in the lower-left corner of the Hopper_mono.mp4 video are in millimeters because I'm allergic to inches. Nevertheless, I left "inches" as the default unit in Hopper Demo_MT.f3d. A little bit of compromise.