TB - I'm unsure what you are calling the yoke??? or what you are asking is rotational ?
The only moving part is the Head, it consists of the two verticals, the treadle, the axle, and what I always called the clamp...
I don't tend to bother with plans for small projects so had never looked for any - So I googled around just now looking for a common nomenclature (I'd been releying on memory of a copy of Woodwrights Shop I haven't opened in ten years - Which doesn't completely apply in that Roy only speaks to the dumbhead pattern common to the Southeast) And found this page -
http://www.greenwoodworking.com/ShavingHorsePlans - Good stuff there
And they call the clamping piece a Yoke - If puts us in the same place, then no, the one pictured is fixed.