SpringConstraint

A SpringConstraint applies a force to its Attachments based on spring and damper behavior. Assuming the constraint has SpringConstraint.Stiffness, it will apply forces based on how far apart the attachments are. If the attachments are further apart than the constraint's SpringConstraint.FreeLength, the attachments will be forced together. If they are closer than the SpringConstraint.FreeLength, the attachments will be forced apart. In addition, if SpringConstraint.Damping is set, there will be a damping component to the applied force that scales with the velocity of the attachments.

This constraint, along with a CylindricalConstraint, is ideal for building vehicle suspension.

Note that if this constraint attaches one part (A) to another part (B) that is anchored or connected to an anchored part (Z), part A will not be locally simulated when interacting with a player.

Calculating SpringConstraint Force

The following helper function exhibits how the force of a SpringConstraint is calculated based on various properties of the constraint and its attachments.

local function getSpringForce(spring)
	if not spring:IsA("SpringConstraint") then
		warn(spring .. " is not a spring constraint!")
		return
	end

	local currentLength = spring.CurrentLength
	local freeLength = spring.FreeLength
	if (spring.LimitsEnabled) then
		currentLength = math.clamp(currentLength, spring.MinLength, spring.MaxLength)
		freeLength = math.clamp(freeLength, spring.MinLength, spring.MaxLength)
	end
	local springLength = currentLength - freeLength

	local axis = spring.Attachment0.WorldPosition - spring.Attachment1.WorldPosition
	if axis.Magnitude > 0 then
		axis = axis.Unit
	end
	local effectiveVelocity = spring.Attachment0.Parent.Velocity - spring.Attachment1.Parent.Velocity

	-- https://en.wikipedia.org/wiki/Harmonic_oscillator
	-- f = -k * x - c * dx/dt + fext
	-- Gravity may not be all of the external forces; friction may affect this, but it's harder to account for
	local forceExternal = Vector3.new(0, -workspace.Gravity, 0)
	local force = -spring.Stiffness * springLength - spring.Damping * axis:Dot(effectiveVelocity) + axis:Dot(forceExternal)

	force = math.clamp(force, -spring.MaxForce, spring.MaxForce)
	return force
end

local function getSpringForce(spring)
	if not spring:IsA("SpringConstraint") then
		warn(spring .. " is not a spring constraint!")
		return
	end

	local currentLength = spring.CurrentLength
	local freeLength = spring.FreeLength
	if spring.LimitsEnabled then
		currentLength = math.clamp(currentLength, spring.MinLength, spring.MaxLength)
		freeLength = math.clamp(freeLength, spring.MinLength, spring.MaxLength)
	end
	local springLength = currentLength - freeLength

	local axis = spring.Attachment0.WorldPosition - spring.Attachment1.WorldPosition
	if axis.Magnitude > 0 then
		axis = axis.Unit
	end
	local effectiveVelocity = spring.Attachment0.Parent.Velocity - spring.Attachment1.Parent.Velocity

	-- https://en.wikipedia.org/wiki/Harmonic_oscillator
	-- f = k * x - c * dx/dt + fext
	-- Gravity may not be all of the external forces; friction may affect this, but it's harder to account for
	local forceExternal = Vector3.new(0, -workspace.Gravity, 0)
	local force = spring.Stiffness * springLength
		- spring.Damping * axis:Dot(effectiveVelocity)
		+ axis:Dot(forceExternal)

	force = math.clamp(force, -spring.MaxForce, spring.MaxForce)
	return force
end

local spring = script.Parent
print(getSpringForce(spring))

Summary