I am creating a wire rope connection for a moving trolley and a spreader which is a part of a container crane. My problem is i can`t create a stable cable system - it always swing. I think the hinge constraints for the sheaves is in free condition. See attached illustration. Is there anyway to stop its large swing movement?
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Given how cables are modelled, it will always be necessary to do something to prevent swinging. The cables themselves can be tuned to have some bending stiffness and damping, but the constraints between the cable segments and pulleys can't apply any moment. So even if you add damping at the sheave's hinge constraint, the cable can still swing freely where it connects to the sheave.
The simplest way to reduce the swinging is to set a Damping Coefficient in the head block or spreader part. This just adds viscous damping to any linear motion of the part. The down side is that it's damping relative to an absolute, static reference, so when the trolley is moved quickly, it might look like the spreader is lagging behind, like it's being pulled through water. You might be able to find tuning that is good enough for you, though, and it's very simple to test.
The most realistic way to damp out the swinging is to add constraints between the head block and the trolley. The constraints can be set to produce damping between the two objects, which will damp out the swinging. And since the damping is between the head block and trolley, if the trolley is moved, the spreader won't lag behind.
More specifically, you can add a Motor constraint which adds just a single constraint in a single direction. The constraint should be aligned so the primary axis is in the direction you want to prevent swinging. The Angular Motor property should be set false (so it's a linear constraint, not angular). Then you can enable friction and set some maximum force, which applies a force resisting motion between the two parts. Then you should probably increase the Loss of the friction, to make the behaviour act more like damping rather than sticky friction.
The motor constraint only constrains one direction, so if you want to constraint swinging in two directions (sideways and forward), you would need two motor constraints.