I can see where this might be used in some situations. But for large applications the cams would be very expensive compared to a hydraulic cylinder. And the platform is unstable unless a follower is used to control the tilt of the table being lifted. This method might be used for very high pressure applications like a press. The cam action could be used for coming up into position quickly and then pressing in at pressures that would be difficult for hydraulic systems to achieve.

Pictures of his proposed apparatus Linear Cam Action

Cams are already used for midsized manufacturing presses. However, the largest presses are all hydraulic.

I stand corrected. The large presses that I've seen were in paper mills and used an electric motor to rotate a cam to raise and lower die at a rate of about one stroke per second. The hydraulic presses they had operated very slowly and were small. After doing a search on the internet, I found toastydeath to be exactly right, almost all of the larger presses are of a hydraulic cylinder type.

This will not lift a given weight with less energy than any other mechanical device. The amount of energy required to lift a given weight any specific distance will be the same no matter how it is levered up(basic physics). The only way to increase the energy efficiency would be to reduce losses due to friction. This device doesn't look like it would have especially low friction. I must admit I'm a little uncertain about how this is suppose to work. It would help if the drawings showed the cams as asymmetrical cams instead of circles. The write-up describes the cams as having a specific decrease in radii, but this is not what is shown in the drawings. However, I think I understand the write-up enough to conclude that this will not work. Sorry.