Show's a Box2D rope joint vs. a distance joint in Corona SDK.

ropeJointvsDistanceJoint.lua

require "physics"
display.setStatusBar( display.HiddenStatusBar )
physics.setDrawMode("hybrid")
physics.start()
physics.setGravity(0, 9.8)
physics.setPositionIterations( 10 )

function getGrapplePoint()
	local point = display.newRect(0, 0, 10, 10)
	physics.addBody(point,"static", {density = 1, friction = .5, bounce = .1})
	return point
end

function getMetalSphere(r)
	local sphere = display.newCircle(0, 0, r)
	physics.addBody(sphere, "dynamic", {density=3, radius=r, bounce=0.0, friction=0.7})
	return sphere
end

local function testingRope2()

	local point1 = getGrapplePoint()
	point1.x = 100
	point1.y = 100

	local point2 = getGrapplePoint()
	point2.x = 300
	point2.y = 200

	local sphere = getMetalSphere(20)
	sphere.x = 0
	sphere.y = 200

	local mappedX, mappedY = sphere:contentToLocal(sphere.x + 2, sphere.y - sphere.height / 2)
	local rope1 = physics.newJoint("rope", sphere, point1, mappedX, mappedY)

	-- now watch the bounce (elsaticity more accurate) of a distance joint
	local sphere2 = getMetalSphere(20)
	sphere2.x = 200
	sphere2.y = 300
	local distance = physics.newJoint("distance", sphere2, point2, sphere2.x, sphere2.y, point2.x, point2.y)
	distance.length = 200
	distance.frequency = 0.7
	distance.dampingRatio = 0

	-- finally, MOVE 'EM UP!
	local t = {}
	t.speed = 5
	function t:timer()
		if rope1.maxLength > 20 then
			rope1.maxLength = rope1.maxLength - self.speed
		end
		if distance.length > 20 then
			distance.length = distance.length - self.speed
		end
	end
	-- t.id = timer.performWithDelay(10, t, 0)

	local function startDrag( event )
		local t = event.target

		local phase = event.phase
		if "began" == phase then
			display.getCurrentStage():setFocus( t )
			t.isFocus = true

			-- Store initial position
			t.x0 = event.x - t.x
			t.y0 = event.y - t.y
			
			-- Make body type temporarily "kinematic" (to avoid gravitional forces)
			event.target.bodyType = "kinematic"
			
			-- Stop current motion, if any
			event.target:setLinearVelocity( 0, 0 )
			event.target.angularVelocity = 0

		elseif t.isFocus then
			if "moved" == phase then
				t.x = event.x - t.x0
				t.y = event.y - t.y0

			elseif "ended" == phase or "cancelled" == phase then
				display.getCurrentStage():setFocus( nil )
				t.isFocus = false
				t.bodyType = "dynamic"
			end
		end

		-- Stop further propagation of touch event!
		return true
	end

	sphere:addEventListener("touch", startDrag)
	sphere2:addEventListener("touch", startDrag)
end

testingRope2()