I went through these two papers. I have a few questions from "Mathematical Analysis of Actuator Forces in a Scissor Lift".

In the Introduction, the author mentioned that the paper is to present the equations for the more general case rather than assuming that one or both of the actuator ends lie along the longitudinal axis of the scissor member. On page 9, the author took two points A and B to derive the equation for l. From Figure 3, it looks like A and B can be any point on the arms and the actuator is a linear actuator. How do I modify the equation stated in this paper to match the following case?

If I use a DC gear motor to turn the screw thread which in turns changes the height of the platform and the motor is attached to the dial like the one shown in the photo rather than attached to the arms.

https://en.wikipedia.org/wiki/Laboratory_scissor_jack