Specific to the term coined in internal combustion engine valve train technology, for automotive, marine, motorcycle and truck engines, where it is being referenced to in this definition, and as set forth originally in the explicative surrounding the Miller mid-lift Patent, #4,365,785 issued to Jim Miller in December 1982, regarding rocker arm geometry: over-arcing (adjective and verb) relates to the radial path which either end of a rocker arm makes as it follows the inherent arc created from a pre-specified distance of measurement from its pivotal axis (the radius), whereby a connection and/or contact is made with respective components: push-rod and valve, both of which operating under linear (in-line) definitions of motion. Although a specific "radius" is designed by this radial length, and could be argued that it is "only" an arc, not truly parabolic (as it is not), the effect of its motion when measured to a linear reference that is fixed, as it relates to the stopping and starting points of this arc, is extremely important to the translation of this radial information, to or from the linear components of which the arc's tangent points attach.
As declared in the MID-LIFT Patent, establishing this pivotal axis for the rocker arm in reference to both the valve tip height and push-rod tip in such a way, for a predetermined length of motion on each, so that a 90 degree relationship of these tangent axis is reached with their respective linear components, exactly when an equal, "half" stroke of motion (mid-lift) has been obtained, will in effect establish the ultimate minimum radial motion on both ends of the rocker arm. Anything else is termed to be "over-arcing," as it inevitably requires a greater period of contact with the respective linear motion components (i.e., push-rod and valve) to effect the same desired linear motion (valve lift). Thus, the rocker arm geometry is stated to be over-arcing.
Specifically though, it should be noted that "over-arcing" in this definition's context relates to one of two variables, dictated by which of two halves the rocker arm's pivotal axis resides in relation to the ensuing motion. In the strict definition, over-arcing pertains to the pivotal axis residing too low with regard to its starting point of motion, in providing a 90 degree relationship at exactly the mid-lift point of motion; whereby 90 degrees is reached (if ever) at some point AFTER the exact half way point of motion (mid-lift) occurs. In the opposite example to this definition, the rocker arm's pivotal axis sits too high with regard to the starting point (valve tip) of motion, thus effecting a sweep of its radial path that dominates beneath itself, whereby the 90 degree relationship of the linear component's axis (valve and push-rod, respectively) to the tangent points to the rocker arm's pivotal axis is acquired BEFORE the mid-lift point of movement is attained. In this example, the term used is under-arcing. As with over-arcing, the result in wasted motion is the same, but the consequences to the ever changing velocity delivered to the valve, which is dictated by where this 90 degree tangent point occurs, is opposite (in both symptoms and effect) to the phenomena of its counterpart. Although both terms are simple in principle, their consequences to the efficient design and implementation of high performance push-rod driven (and otherwise) valve trains is decisive.