It's excellent that you're digging deeper into the fascinating biomechanics of horse locomotion! You're right to focus on the dynamic nature of the forelimb's center of rotation (CoR). Since the horse's forelimb isn't anchored by a clavicle but suspended by the muscular thoracic sling, the scapula (shoulder blade) can perform complex movements – it both slides along the ribcage (translates) and rotates. This means the CoR isn't fixed but moves continuously throughout the protraction phase.

We can think of this moving center as an Instantaneous Center of Rotation (ICR) – the point around which the limb appears to be pivoting at any given instant. While mapping its exact path requires sophisticated equipment, we can describe its general behavior during forelimb protraction (when the hoof is off the ground and swinging forward):

1. Lift-Off & Early Protraction:

• Scapular Action: As the hoof lifts off the ground, the Serratus ventralis muscle (a key part of the thoracic sling) contracts, helping to lift the shoulder girdle and initiate the forward swing. The scapula begins to slide forward and rotate. The top (dorsal) border of the scapula moves forward, while the bottom (where the shoulder joint sits) also moves forward and slightly upward.
• Shoulder Joint Action: The shoulder joint (glenohumeral) starts to extend (open up).
• Approximate ICR Location: At this very early stage, the ICR can be thought of as being located relatively high up on the scapula, perhaps within its upper third. This is because the initial movement is largely driven by the muscles controlling the scapula's position relative to the trunk. It's the "pivot" for the entire limb structure beginning its swing relative to the horse's body.

2. Mid-Protraction (Maximum Forward Velocity):

• Scapular Action: The scapula continues its forward slide and rotation. It's moving significantly along the ribcage now, contributing substantially to the reach of the limb.
• Shoulder Joint Action: This is when the primary protractor muscles, like the Brachiocephalicus, are very active, pulling the humerus (upper arm bone) strongly forward. This causes significant extension at the shoulder joint.
• Approximate ICR Location: As the shoulder joint extends and the scapula slides and rotates, the ICR effectively moves. It's no longer just a high point on the scapula; it follows a curved path. Imagine a point moving both forward (with the scapula's slide) and downward relative to the top of the scapula as the shoulder joint opens. It's within the 'cloud' of the upper/mid-scapula but its effective position relative to the limb segments below is constantly changing. The CoR of the scapula itself is often considered to be around the insertion point of the Serratus ventralis, but the CoR of the entire limb is influenced by both scapular movement and shoulder joint movement.

3. Peak Protraction (Maximum Forward Reach):

• Scapular Action: The scapula has reached its most forward (cranial) and most rotated position for this stride.
• Shoulder Joint Action: The shoulder joint is at its maximum extension for the swing phase. Muscles like the Biceps brachii have contributed, storing and releasing energy to help 'snap' the lower limb forward.
• Approximate ICR Location: At the very peak of protraction, just before the limb starts its backward swing (retraction) to prepare for landing, the ICR has reached its most forward and potentially lowest point in its path relative to its starting position. The entire structure is "laid out" in front.

In essence:

Think of the scapula as a large, flat bone sliding on a curved surface (the ribcage) while also spinning. The shoulder joint acts as a hinge at the bottom of this sliding/spinning bone. The "center of rotation" for the entire limb isn't a pin in the middle of the scapula; it's a virtual point that moves because both the scapula's position and the shoulder joint's angle are changing simultaneously.

This complex, dynamic system, allowed by the thoracic sling, is a key adaptation for equine locomotion. It significantly increases stride length by allowing the entire pivot point to move forward, enabling horses to cover ground efficiently and athletically.