[Daryl]

Nice post. Forgive me for trying to steer this to what I think of as "The Circle" and its Low-Point Geometry. Your post is very insightful regarding how Hinging changes as the Plane Angle changes but I think you're getting ahead of the Basic idea of the Geometry of the Circle. It's a very simple but profound subject regarding Golf Club design and an Orbiting clubhead and why we humans are so successful at hitting a ball with a club.

When I think of the Geometry of the Circle , what seems to me, its basic form, outlined below.

Imagine an Orbit on a Horizontal Plane.

It represents an On-Plane Force (Stick without a club-head) moving around and around while striking a ball anywhere on the orbit without having any different ball response. When a Flat Striker is introduce, the response will be the same for direction. Then, when we angle (incline) the Striker, we'll see the same response for direction because the ball will rebound at right angles to the "Force" but in addition, it will rebound at right angles to the Inclined Striker (Loft). The Loft creates a Vertical Plane to the "Horizon" (considering a Horizontal Orbit).

When the Orbit is inclined (Inclined Plane), the Plane of the Loft becomes a tilted Vertical Plane (Tilted to the Horizon) but the ball response remains the same while struck at any "Point" on the orbit. The ball shoots off on a trajectory above the circle relating to how much the Orbit is Inclined and gravity pulls it downward from its Plane. When the Lofted Striker is re-oriented so that the Loft Plane is Vertical to the Horizon,it Will only be Vertical to the Horizon at one point on the Orbit. This creates what we call "Lie Angle". Although the Ball response remains the same, we have a "Point" on the Orbit, when aligned to a target, will produce the desired straight shot (given an elastic collision). HK called this, where all of these Alignments converge, "Low Point". The Striker Alignment is tangent to the circle (Horizontal, direction) and only at the bottom would it align to the Target. And, we have a Stick (Force) with a Lofted Striker, at Right Angles to the Tangent. Rightly so, we now have "Low Point" Geometry and it is at the Bottom of the Inclined Orbit.

So, Geometry of the Circle, is about the Orbit, of an aligned inclined striker Force, and where on the orbit, it produces the ball response we want. So, a Low Point Impact is what will achieve our goal. Playing the Ball before Low Point Geometry is very attainable because the inclined striker and plane angle can be changed to reproduce the Straight Away Alignments of Low Point.

After understanding the "Circle", we apply tools such as Hook-Face to accommodate Ball Location Changes. Hook Face is another subject. It dramatically changes Alignment and the way the Clubface closes. We should explore this along with Plane Angles and Ball Location. These are changes that accommodate Ball placement changes on the Circle.

Hinge Action is method we use to control the Ball's "inelastic" collision. The Ball can respond to an angular force as though it were struck with a linear force. Hinging adjusts to the Circle as well as Hook Face.

Hook-Face is the way we re-align the equipment, the Right Forearm Angle of Approach and Hinging is the way we re-Align the Machine.