Understanding Pulleys in Mechanical Advantage Systems

How Pulleys Work

• Fixed Pulleys: Function as first-class levers with the fulcrum located at the axle of the sheave. They change the direction of force without increasing MA. For instance, a change-of-direction pulley has an MA of 1:1.
• Moving Pulleys: Act as second-class levers, where the rope is attached to the anchor, and the load hangs below the pulley. These pulleys increase the MA, typically at a ratio of 2:1.

How Pulleys Work

A fixed pulley can be viewed as a first-class lever. The fulcrum is located at the axle in the center of the sheave, directly below the carabiner that connects the pulley to the anchor point. Because the sheave is round, the distance (FR) from the axle (fulcrum) to the point the rope leaves the sheave and goes to the resistance (load) is equal to the distance (FE) from the axle to the point that the rope leaves the sheave and goes to the effort (force). The two lever arms are equal, resulting in 1:1 MA and the reason a change-of-direction pulley does not increase the mechanical advantage of the system. 

A moving pulley can be viewed as a second-class lever. The fulcrum is located on the edge of the sheave directly below the point where the rope is attached to the anchor. One lever arm (FR) extends from the fulcrum to the pin, which is directly above the carabiner that attaches the resistance (load) to the pulley. The other lever arm (FE) extends from the fulcrum to the point where the rope leaves the sheave and goes to the effort (force). This lever arm is twice as long as the other arm, resulting in 2:1 MA. Moving pulleys increase the mechanical advantage of the system. 

Applications of Pulleys in MA Systems

1. Fixed or Change-of-Direction Pulleys:
   Used to redirect the force applied, optimizing the hauling field without altering the load’s MA.
2. Movable or Mechanical Advantage Pulleys:
   Attached to the load to reduce the input force required to lift the load, amplifying efficiency in the system.
3. Ratchets or Progress Capture Devices (PCD):
   Prevent the load from sliding back when the pulling force is released. Devices like mechanical rope grabs or prusik loops are often used as ratchets to reset the MA system for further hauling.

Pulleys in Mechanical Advantage Systems

Pulleys perform two distinct functions in mechanical advantage systems. If the pulley is attached to the anchor, it is called a fixed or change of direction pulley. Its job is to change the direction of pull on the rope. If the pulley is attached to the load, it is a movable or mechanical advantage pulley. Its job is to increase the mechanical advantage of the system. 

A ratchet, also called a progress capture device or PCD, is a device that, when attached to an anchor, will hold the rope so that the load will not lower back down when the pulling force is released. This acts as a safety so the load will not fall back down if the haul team lets go of the rope. This also allows us to reset the mechanical advantage pulleys so we can haul the load further. The number of times that a raising system will need to be reset will depend on the distance the load must be raised and the distance the raising system can be extended. A mechanical rope grab, or a friction knot tied with a prusik loop can be used as a ratchet. 

By building systems using different combinations of mechanical advantage pulleys, change of direction pulleys, rope, anchors and ratchets, we can come up with the right tool for the specific job we need to accomplish. Generally, using the lowest mechanical advantage needed to get the job done will result in the quickest rescue because it requires fewer resets. 

For simplicity, this blog we will ignore the friction inherent in these systems and focus on theoretical mechanical advantage. Theoretical vs. Actual Mechanical Advantage will be covered in future blogs. 

Simple Pulley Systems

Simple M/A systems can be defined as systems with all the moving pulleys moving in the same direction and at the same speed as the load. A few simple pulley systems are most frequently used. The most common is a 3:1 mechanical advantage, sometimes called a “Z” rig because when rigged, the rope looks like a “Z”. In theory, a 100-pound pull would raise a 300-pound load. Due to friction, the actual mechanical advantage is slightly lower. 

Many confined space operations require a vertical entry. When we build a mechanical advantage system to move a load in this situation, a simple “Block and Tackle” system such as a 2:1 “Ladder Rig” or a 4:1 with double sheave pulleys at the top and bottom can be used. 

Compound Pulley Systems

Compound pulley systems are created when a simple pulley system is pulling on another simple pulley system. By adding a 2:1 mechanical advantage to a 3:1 mechanical advantage system you compound, or multiply, the mechanical advantage and end up with a 6:1. A 3:1 pulling on another 3:1 gives you a mechanical advantage of 9:1. 

Complex Pulley Systems

A system that is neither simple nor compound is a complex pulley system. The 5:1 shown is a complex system.

Types of Mechanical Advantage Systems

1. Simple Pulley Systems

• Definition: Systems where all moving pulleys travel in the same direction and at the same speed as the load.
• Example: A 3:1 MA system or “Z-rig,” often used for confined space vertical rescues. A 100-pound input force can theoretically lift a 300-pound load, though friction reduces the actual MA slightly.

2. Compound Pulley Systems

• Definition: Created by combining simple systems, compounding the MA.
• Examples:
  • 3:1 pulling a 2:1 results in a 6:1 MA.
  • 3:1 pulling another 3:1 creates a 9:1 MA.

3. Complex Pulley Systems

• Definition: Neither simple nor compound, complex systems often provide higher efficiency.
• Example: A 5:1 complex system achieves the same output with fewer pulleys and less friction than a simple 5:1.

Piggyback Systems

Another method that can be used is a “piggyback”, which is a mechanical advantage system on a haul line. The load is supported on a separate rope held by a ratchet, and a pre-rigged mechanical advantage system is connected to the haul line with a prusik hitch when the load needs to be raised. This can be helpful in situations where the load is raised and lowered back and forth several times. Piggyback systems can be of any level of mechanical advantage. While not common, piggyback lowering systems can also be rigged. They are usually used for short distances or when passing a knot.  

Specialized Techniques

Piggyback Systems

• Attach a mechanical advantage system to an independent haul line.
• Useful for repetitive raising/lowering tasks or passing a knot in the line.
• Piggyback systems can also be adapted for short-distance lowering scenarios.

The T-Method

• A universal method for calculating theoretical MA.
• Steps:
  • Start with 1 unit of tension at the input end.
  • Add tensions as they enter and exit each pulley.
  • Sum the tensions at the load to determine the MA.

Practical Considerations

• Minimize the use of unnecessary pulleys to reduce friction.
• Opt for the lowest MA required to complete the task efficiently.
• Test the system thoroughly to ensure safety and reliability under load.
• Incorporate ratchets and backup systems for added security.

Common Equipment Used

• CMC Pulleys: Reliable for both fixed and movable pulley applications.
• Petzl Pro Traxion: A popular PCD for progress capture.
• Prusik Knots: Often used in lightweight, versatile systems.

Key Takeaways

1. Use the simplest MA system suitable for the task to reduce resets and friction.
2. Understand the roles of fixed and movable pulleys for optimal system design.
3. Combine systems creatively (compound or complex) to meet challenging rescue scenarios.

For more advanced training, explore the Rigging Lab Academy Pulley Systems Course and discover a range of practical applications tailored for technical rescue teams.

Where To Get CMC Pulleys 

Peace on your Days

Lance