Minimalist Pinch Table | Seek n' Geek VII

Tables and furniture became a theme of my thinking this term, inspired by the class project. While looking for inspiration for my transforming table I came across this table called the Mantis explained on Instructables. The author, planesdesign, describes how a human hand was the inspiration for his minimalist pinch design that supports this table top. Opposable thumbs are essential tools for humans, and the pinch between the thumb and fingers is surprisingly strong (especially in climbers). The design of this desk uses a similar "pinch" mechanism that is really two different mechanisms -- the pinch that keeps the long length of the table horizontal, and the pinch that keeps the short width of the table stable. Both mechanisms use opposing forces and moments to achieve stability.  


Figure 1: The Mantis desk

To better understand the member sizing and stability of this structure I did first level static analysis, and stress analysis of a joint to validate my own material design choices. I also calculated the basic geometry to achieve a desired height and leg spacing.


The calculation to the right, shows the geometric relationship between the spacing and sizing of the pinchers, the thickness of the table top (assumed here to be 2x4 lumber) and the overall height of the table based on total leg length.

Figure 3 below shows my first thoughts as I started thinking through what was going on and how did I want to analyze the structure. Initially, I wasn't sure whether I should analyze one leg or the whole system, but decided to analyze the entire structure, because it is only static when the two legs are attached to the table. 

At the end of this sheet, I realized one of the questions I needed to answer was, does F1 = F2?  My calculations and sketches below show how I calculated F1 and F2 in the upper left hand corner using force and moment balances, with an assumption that the table top was constrained by a pin joint.  Looking at the left bottom corner shows the distinction between shear and bending acting on the two arms of the pinch mechanism, and incorporates the values for F3 and F4 calculated in the center diagram. Finally, the right column shows a sideview full structure analysis to determine bending of the diagonal leg.  

The primary sources of error in this table are geometric and structural errors. Structural beam bending and shearing, and geometric pinch spacing which propagates into the leg angle, table height, and the overall leveling of the table. Gravitational preload instigates the pinching that stabilizes the table top. If I were actually building this desk I would also want calculate the "softness" of the material I used for the wood top and the forces applied along the pinch arms to make sure that the pinching force didn't visibly compress the material.