In a 'pendulum' stroke with the forearm straight down as the rod of a pendulum would be & with the elbow fixed as a pivot point, & with the cue tip very near the cue ball, the cue is pulled back which requires the hand & the contact point of the cue at the hand to rise up as the hand travels along the arch as created by the fixed elbow (pivot point) & the forearm (pendulum rod). When that happens the cue tip also follows a smaller arch as it moves downward. Then in the forward part of the stroke, the hand & the contact point on the cue follow the path of the pendulum arch in the opposite direction back down to the position where the forearm (pendulum rod) are again straight down & perpendicular to the path of travel. During that timeframe the cue tip has followed it's arch on a reverse path & has come back up to very near the ball. Then as the hand & cue contact point of the cue goes forward it archs up which causes the cue tip to arch downward through the cue ball & toward the cloth.
That is my understanding of the simple pendulum stroke.
If one alters one's grip & wrist or allows one's elbow to drop a bit on the back stroke & then reverses going forward to contact & then again on the finish or follow through the cue can move is a straight line 'piston like' movement. If one does these things then one is employing a straight line 'piston stroke' & not a pendulum stroke.
What is it that I do not understand? Can there be components of both strokes intermingled? Yes to some degree & that is why it is the path of the cue stick that is the telling factor.
If one is not set up properly, it would probably require an elbow drop before contact to accomplish a straight line piston movement. But if one is set up properly it could look very much like a pendulum stroke but not be so. The path of the cue is the telling factor not the movement of the body parts. Now if one sees significant elbow drop on the back swing it would probably be an indication of a scissor motion & a piston type stroke but not if the hand comes up on the forward side of the straight down arm. The point of this is that a combination of set up & arm motion are not definitive indicators of the actual stroke. It is the movement of the cue that differentiates what the stroke actually was, a straight in line piston or the slight rocking of the cue up, down, up or down, up, down depending on which end of the cue one is describing for a pendulum stroke.
If the back stroke is like the pendulum & the forward stroke has an elbow drop through the ball then I believe that is called a J-piston or piston-J stoke
If I don't understand something, I'm open for informative correction.