I'm trying to resolve a situation of characters being connected to things that are moving. If I am at the end of a 20ft chain connected to a boulder, and someone drops that boulder off a 50ft cliff, presumably that would pull me over as well, wouldn't it? Effectively I would be restrained, but could move freely within the length of the chain. What is the best way to model this in the system?
You can use normal forced movement rules to get them to the precipice, but the PC should get a saving throw (Rules Compendium p. 213, DMG p.44) to avoid going over the edge.
If they succeed on their save, the Climbing rules should take effect, because the PC has fallen prone at the edge with a massive boulder pulling them down. If they fail, they take 1d10 falling damage per ten feet fallen, with an Athletics check to resist some damage (PHB p.284).
If they make their saving throw at the precipice, they fall prone and the boulder gets to pull really really hard on the chain. I would improvise this as an attack-with-combat-advantage against FORT. Even though the player is prone, I would model it as placing the player in the climbing state, with the weight of the boulder substituting for the pull of gravity.
If they have sufficient FORT, they can shrug off the damage and hang on; if not, damage forces them to make an Athletics check at DC-plus-damage-taken to hold on and not be moved. (PHB p.182 for all climbing rules incl. damage while climbing). If the boulder exceeds a player's maximum drag load (50x STR, PHB p.222) then the damage should be static and push the DC to the point where only a critical hit will work. If the boulder exceeds 20xSTR, then the player is both slowed (speed = 2) and climbing (climb at half speed on a success) so even a successful climb check will likely have them moving only one square per turn.
From here, then, you can adjust the terrain climb DC, the boulder's attack, and the boulder's weight and damage numbers with an understanding of how hard you want it to pull on your players. In particular you can look at your PCs' Athletics and FORT scores to figure out their odds of surviving.
DMG p.65 lists object defenses and hit points; Iron Manacles have a FORT of 8 (auto-hit for most PCs) and 30 hps, so it's possible for the player to break the chain in order to free themselves. A sufficiently-motivated ranged striker could break the chain with an encounter or daily power and some lucky dice rolls.
You just described how to model it: The character is unable to move 20ft away from the bolder, and movement of the boulder is, effectively, a type of forced movement (lagging 20ft) for the character.
You should probably include some way for the character get free, whether it be strength checks, a bunch of help, or a hammer and chisel.
You should model it as forced movement (does not provoke opportunity attacks). However unless you can justify stopping the boulder you are falling with it.
You now take 5d10 falling damage unless you are trained in acrobatics, in that case you can reduce the damage by the amount of an acrobatics check divided by 5(I think).
I would make a generic rule that still allows a small measure of player agency.
Any time the boulder moves to a square more than 4 squares away from you, you must shift as a free action to remain within 4 squares of the boulder.
This allows the character to look around frantically and attempt to shift diagonally so the chain gets snagged on something strong enough to hold the boulder up. Or maybe even get a free chance to knock an enemy prone with the chain.
But if nothing is around (and this is the best part) you can rub your hands together and laugh derisively as the player is forced to utter the words: "I shift off the cliff."
You're asking half a physics question, half a D&D question, so here's half a physics answer, half an RPG answer:
Let's say you and the boulder are standing right next to each other at the edge of a 50 ft. cliff. There's a 20 ft. chain from an iron ring around your...neck? waist? Let's say waist. A troll comes along and pushes the boulder over the edge of the cliff.
The boulder falls 20 ft, and then you get yanked off the cliff. This takes 1.1 seconds, and is like getting punched in the stomach by an iron bar moving 24 mph. See wolfram alpha for all the calculations.
When you hit the ground, about 1 second later, you'll hit the ground at about 46 mph - the boulder was going 39 when it hit the ground, and so were you. You have however long it takes to travel that remaining 20 feet to accelerate to your final speed. That's gonna be about 46 mph. I had help on this math, so don't ask me for all the details. I also made all sorts of simplifying assumptions, like no air resistance, and the boulder's mass is so much greater than the PC's that the loss of velocity for the boulder was essentially zero.
So much for the physics answer. For the RPG, I would do this:
1) Apply damage for the boulder yanking him off the cliff. 2) Apply damage for hitting the ground.
Does DnD have collision damage? Probably not. Use falling damage instead.
So at the table, in lieu of doing all this math, I'd probably have just said:
"Ouch! The boulder yanks you off the cliff, and then you slam into the ground below! Roll for damage for falling 50 feet and add 50%. Armor does not protect."