SpriteKit stop spinning wheel in a defined angle - ios

Question

I have a spinning wheel rotating at an angular speed ω, no acceleration involved, implemented with SpriteKit.
When the user push a button I need to slowly decelerate the wheel from the current angle ∂0 and end-up in a specified angle (lets call it ∂f).
I created associated to it a mass of 2.
I already tried the angularDamping and the SKAction.rotate(toAngle: duration:) but they do not fit my needs because:
With the angularDamping I cannot specify easy the angle ∂f where I want to end up.
With the SKAction.rotate(toAngle: duration:) I cannot start slowing down from the current rotation speed and it doesn't behave natural.
The only remaining approach I tried is by using the SKAction.applyTorque(duration:).
This sounds interesting but I have problems calculating the formula to obtain the correct torque to apply and especially for the inertia and radius of the wheel.
Here is my approach:
I'm taking the starting angular velocity ω as:
wheelNode.physicsBody?.angularVelocity.
I'm taking the mass from wheelNode.physicsBody?.mass
The time t is a constant of 10 (this means that in 10 seconds I want the wheel decelerating to the final angle ∂f).
The deceleration that I calculated as:
let a = -1 * ω / t
The inertia should be: let I = 1/2 * mass * pow(r, 2)*. (see notes regarding the radius please)
Then, finally, I calculated the final torque to apply as: let t = I * a (taking care that is opposite of the current angular speed of the wheel).
NOTE:
Since I don't have clear how to have the radius of the wheel I tried to grab it both from:
the wheelNode.physicsBody?.area as let r = sqrt(wheelNode.physicsBody?.area ?? 0 / .pi)
by converting from pixel to meters as the area documentation says. Then I have let r = self.wheelNode.radius / 150.
Funny: I obtain 2 different values :(
UNFORTUNATLY something in this approach is not working because so far I have no idea how to end up in the specified angle and the wheel doesn't stop anyway as it should (or the torque is too much and spins in the other direction, or is not enough). So, also the torque applied seems to be wrong.
Do you know a better way to achieve the result I need? Is that the correct approach? If yes, what's wrong with my calculations?

Answer 1

Kinematics makes my head hurt, but here you go. I made it to where you can input the amount of rotations and the wheel will rotate that many times as its slowing down to the angle you specify. The other function and extension are there to keep the code relatively clean/readable. So if you just want one giant mess function go ahead and modify it.
• Make sure the node's angularDampening = 0.0
• Make sure the node has a circular physicsbody
// Stops a spinning SpriteNode at a specified angle within a certain amount of rotations
//NOTE: Node must have a circular physicsbody
// Damping should be from 0.0 to 1.0
func decelerate(node: SKSpriteNode, toAngle: CGFloat, rotations: Int) {
if node.physicsBody == nil { print("Node doesn't have a physicsbody"); return } //Avoid crash incase node's physicsbody is nil
var cw:CGFloat { if node.physicsBody!.angularVelocity < CGFloat(0.0) { return -1.0} else { return 1.0} } //Clockwise - using int to reduce if statments with booleans
let m = node.physicsBody!.mass // Mass
let r = CGFloat.squareRoot(node.physicsBody!.area / CGFloat.pi)() // Radius
let i = 0.5 * m * r.squared // Intertia
let wi = node.physicsBody!.angularVelocity // Initial Angular Velocity
let wf:CGFloat = 0 // Final Angular Velocity
let ti = CGFloat.unitCircle(node.zRotation) // Initial Theta
var tf = CGFloat.unitCircle(toAngle) // Final Theta
//Correction constant based on rate of rotation since there seems to be a delay between when the action is calcuated and when it is run
//Without the correction the node stops a little off from its desired stop angle
tf -= 0.00773889 * wi //Might need to change constn
let dt = deltaTheta(ti, tf, Int(cw), rotations)
let a = -cw * 0.5 * wi.squared / abs(dt) // Angular Acceleration - cw used to determine direction
print("A:\(a)")
let time:Double = Double(abs((wf-wi) / a)) // Time needed to stop
let torque:CGFloat = i * a // Torque needed to stop
node.run(SKAction.applyTorque(torque, duration: time))
}
func deltaTheta(_ ti:CGFloat, _ tf:CGFloat, _ clockwise: Int, _ rotations: Int) -> CGFloat {
let extra = CGFloat(rotations)*2*CGFloat.pi
if clockwise == -1 {
if tf>ti { return tf-ti-2*CGFloat.pi-extra }else{ return tf-ti-extra }
}else{
if tf>ti { return tf-ti+extra }else{ return tf+2*CGFloat.pi+extra-ti }
}
}
}
extension CGFloat {
public var squared:CGFloat { return self * self }
public static func unitCircle(_ value: CGFloat) -> CGFloat {
if value < 0 { return 2 * CGFloat.pi + value }
else{ return value }
}
}