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harness saddle

n. An element of horse harness which supports the weight of shaft or poles attaching a vehicle to a horse.

Wikipedia
Harness saddle

A harness saddle is an element of horse harness which supports the weight of shafts or poles attaching a vehicle to a horse. Like other types of saddle, it lies on the horse's back directly behind the withers, often has an internal supportive framework, often called a saddle tree, and usually is secured on either side by a girth passing beneath the horse. Unlike riding saddles, it is an integral part of the harness and is not used as stand-alone equipment.