initial design

After reviewing the current designs available and considering several new design ideas of our own, we finally settled on what we tentatively called a "modified ubrella anchor design."

Modified Umbrella Anchor Design:

Here was our initial design concept for the modified umbrella anchor.

It worked, theoretically at least, by expanding just like an umbrella inside a crack to bring the contact surfacew, shown as aluminum pads mounted at the ends of the arms on a ball joint, in contact with the wall of the crack. The support arms connected to actuator arms which were in turn connected to a trigger of some sort. The trigger acted against either a linear spring (right) or against two torsional springs (left), which would bring the support arms into position and set the anchor in the crack. By only having two arms, and incorporating the pivoting pads, we hoped to eliminate walking from our design completely.

After much debate over the details of the design, we decided to build a crude model to test or ideas and to prove the concept.

The Models:

stage 1

This was the first stage of development of the model.

The umbrella anchor started out with two independent arms, which pivoted when actuated with a wire trigger. This, when modeled, proved to be unstable.

stage 2

The second stage in our evolutionary process was to replace the wire actuator with a rigid actuator arm. This caused the arms to be dependant. Although this added some stability to our model, the anchor could still be easily removed from a crack.

stage 3
In the third stage, pivoting feet were then added. When these did not significantly increase the force needed to poll the anchor out of the crack, calculations were then done on the umbrella anchor design.

Which brings us to our next topic...

Friction Force (the Epiphany):

We knew there had to be a reason a design as simple and obvious as this one wasn't already out there being used.

Well... here's why.

What you see above is a free body diagram of our umbrella anchor. When the climber falls, he or she exerts a force P on the device. This force is transmitted to the wall of the crack down the support arms of the device as M, which then translates into a normal force N perpendicular to the crack wall.

In order for the any frictional anchor to be effective, it must somehow generate a large enough normal force N as a result of P to create an opposite friction force F against the wall of the crack to counter-act P.

With a friction factor of aluminum against rock of approximately µ = 0.3, this means that the angle theta must be greater than 74 degrees in order to create a large enough F to support a 13kN (2900 lb) load!

With the 7cm arm lenght that we had designe and build in the model, that meant that the effective crack size range for our design was around 5 mm!

This is the reason that SLCD's work. The logarithmic spiral design of the cam lobes ensures that the angle of transmission theta is always constant (and greater than 74 degrees). This is covered in greater detail in the secondary design page.

The Models:
stage 1	This was the first stage of development of the model. The umbrella anchor started out with two independent arms, which pivoted when actuated with a wire trigger. This, when modeled, proved to be unstable.
stage 2	The second stage in our evolutionary process was to replace the wire actuator with a rigid actuator arm. This caused the arms to be dependant. Although this added some stability to our model, the anchor could still be easily removed from a crack.
stage 3	In the third stage, pivoting feet were then added. When these did not significantly increase the force needed to poll the anchor out of the crack, calculations were then done on the umbrella anchor design.