Design
The picture shows the fourth physical incarnation of essentially the same antenna - A pair of two element yagis mounted at right angles and fed 90 degrees out of phase using a quarter wave of coax.
Design optimised on polar diagram and gain.

Construction
Two versions were constructed from 8mm microbore central heating pipe and 40mm waste pipe. The other two (including the one pictured) used copper wires twisted together using an electric drill. Twisted wire elements tend to droop a little as can be seen but this doesn't seem to seriously affect performance.

Construction Notes
These notes are brief as there is nothing especially taxing with the construction...
It is advisable to fit a short length of plastic rod between the dipole halves when using 8mm tube and a short length of plastic tube with a cutout for soldering the connections over the twisted wire in those versions.

A "dirty balun" should be formed by taking the coax through the tube wrapping it around 5 times and then taking it inside to make the connections. The necessary holes should be marked and drilled before connecting the coax.

Polarisation
To achieve the necessary right hand circular polarization one dipole of the pair is fed through a quarter wave of coax from the feed point of the other. This diagram should make plain where the inners need to go. Getting this wrong will result in left hand circular polarisation and an antenna that doesn't work.

Dimensions
Dipole: 99cm (8mm tube) 100cm (twisted wire)
Reflector: 106cm
Spacing: 39cm
1/4 wave delay line - I used 75ohm TV Coax and using the MFJ analyser the length worked out to 39.5cm.

Here are the EZNec plots of a two element yagi with these dimensions. Lack of skill and laziness mean I haven't produced a plot for the complete turnstile.