What is an Open Sleeve Multi-Band Yagi Design?

I have been using my Moxon Yagi for LEO satellite operations for a few months now. It has a single driven element which is a Moxon driven element for VHF. UHF elements are passively coupled, without a connection to feed line for any of the elements. Today I came across the term Open Sleeve Yagi as a comment on YouTube. A search for the term brought me to the QSL net page of DK7ZB on Sleeve and Open Sleeve elements for Yagi antenna. He mentioned that if a tube of shorter length than the driven element is pushed over it, there is another resonant frequency F2 in addition to F1 of the driven element. This tube has been called as the Sleeve. To simply design, instead of a tube element, keeping two skeleton elements close by and one in front and back of the driven element gives a similar additional resonance at F2. As the next step in derivation, using a single skeleton element gives the Open Sleeve design. The length of the skeleton element will determine the frequency F2 while the separation from the driven element will determine the radiation resistance and there by the impedance on F2.

Looking back on the design of my Moxon Yagi, it has a UHF element which is very close to the VHF Moxon driven element and passively coupled to it. So I presume that the Moxon Yagi is also having an Open Sleeve design, though the VHF driven element is not straight and kept folded so that along with the reflector element it forms the Moxon Rectangle for VHF. The VHF driven element resonates as 3/2-lambda for UHF. This along with the parasitic fed UHF element will give more directional gain. Highest current will be in a parasitically fed Open Sleeve UHF element! In fact, I had started assembling 5+8 element dual band yagi of DK7ZB design some time back, for better gain than the Moxon Yagi. That project is still in cold storage, mainly because of my worry that increasing gain would decrease beamwidth of antenna and reduce time window for operation in a given satellite pass as I do not have an antenna rotator. Looking back, that design is also Open Sleeve.