I think the most straightforward approach to create a relationship between the solenoid displacement to the catapult arc would be as follows (starting at the profile view of the mechanism shown at 4:07): The horizontal displacement of the solenoid will be referred to as “deltaX”. The length of the arm that extends from the pin to meet the dowel representing the solenoid I will call “e”. This is the measured distance from the center of the pin to the wooden dowel’s point of contact. The length of the catapult arm itself is “r” and the arc length it traces will is “s”. First, we are after the angular displacement of the mechanism, “Theta”. I envision that the values of “e” and “deltaX” form a right triangle when the solenoid is activated. We can exploit this geometry using a trigonometric relationship to compute an angular displacement, “theta”, for any “deltaX” or “e”. The formula would look something like this: theta = arcsin(deltaX/e) (Eq. 1) When calculating inverse sine (arcsine or sin^(-1)) be sure the calculator is in radians. The next formula takes radians by default. Since the catapult is a rigid body, the displacement we calculate here is also the displacement of the catapult arm itself. Second, we can invoke the definition of circular arc length to compute the distance traveled at the end of the catapult arm: S = Theta*r(Eq. 2) Substituting Eq. 1 into Eq. 2 we get the formula for S: S = arcsin(deltaX/e)*r To compote the amplification between the solenoid displacement and the catapult angular displacement ratio: S/deltaX This ratio may also be thought of as the ratio between the linear velocity of the solenoid and the tangential velocity of the projectile in the catapult bucket.
Hello sir, I don't think you'll probably see my comment but just wanted to say that I just stumbled upon your channel again, I remember watching your videos when I was a kid and I was trying to make my own paper weapons/armor haha, you managed somehow to give me that spark in creativity back in those days :). Wish you the very best. Have a nice day.
I was imagine I like to mechanicals like that when I get a shop, I’ll make a cannibal some of these days and do awesome things in dungeons and dragons games or Knight tale 😊 so glad to see you on your RUclips videos will 👍🏻
I've been with you for years man I love the swords and shields type things.i often have dreams of being a knight back in the past .sorry I can't support you with money but I support you with my heart brother stay safe 🙏
I think the most straightforward approach to create a relationship between the solenoid displacement to the catapult arc would be as follows (starting at the profile view of the mechanism shown at 4:07):
The horizontal displacement of the solenoid will be referred to as “deltaX”. The length of the arm that extends from the pin to meet the dowel representing the solenoid I will call “e”. This is the measured distance from the center of the pin to the wooden dowel’s point of contact. The length of the catapult arm itself is “r” and the arc length it traces will is “s”.
First, we are after the angular displacement of the mechanism, “Theta”.
I envision that the values of “e” and “deltaX” form a right triangle when the solenoid is activated. We can exploit this geometry using a trigonometric relationship to compute an angular displacement, “theta”, for any “deltaX” or “e”.
The formula would look something like this: theta = arcsin(deltaX/e)
(Eq. 1)
When calculating inverse sine (arcsine or sin^(-1)) be sure the calculator is in radians. The next formula takes radians by default.
Since the catapult is a rigid body, the displacement we calculate here is also the displacement of the catapult arm itself.
Second, we can invoke the definition of circular arc length to compute the distance traveled at the end of the catapult arm: S = Theta*r(Eq. 2)
Substituting Eq. 1 into Eq. 2 we get the formula for S:
S = arcsin(deltaX/e)*r
To compote the amplification between the solenoid displacement and the catapult angular displacement ratio:
S/deltaX
This ratio may also be thought of as the ratio between the linear velocity of the solenoid and the tangential velocity of the projectile in the catapult bucket.
Wow. Stunningly well explained. My gratitude to you for the work you put in. Thanks!
I am pinning this comment to the top so viewers can see it and get the benefit of it.
That's awesome Will
Thanks Carl! Great to hear from you!
Hello sir, I don't think you'll probably see my comment but just wanted to say that I just stumbled upon your channel again, I remember watching your videos when I was a kid and I was trying to make my own paper weapons/armor haha, you managed somehow to give me that spark in creativity back in those days :).
Wish you the very best.
Have a nice day.
I was imagine I like to mechanicals like that when I get a shop, I’ll make a cannibal some of these days and do awesome things in dungeons and dragons games or Knight tale 😊 so glad to see you on your RUclips videos will 👍🏻
Sounds like a great plan. It will be fun!!
I've been with you for years man I love the swords and shields type things.i often have dreams of being a knight back in the past .sorry I can't support you with money but I support you with my heart brother stay safe 🙏