# Constant-force actuator for a lifting plate

Thank you for this forum. I am writing here because I struggle with a mechanics problem. I am designing a lifting device for heavy charges. The load (F) is applied to a top plate. I would like this top plate to be lifted from an initial altitude z_topplate(t=0) to a certain altitude z_topplate(t=tf). There are two major constraints:

• There isn't much space between the top plate and base plate (at altitude z_baseplate).
• Actuator or motor should be contained between bars at all time, so between z_baseplate and z_topplate(t). I can't put them lower than z_baseplate and over z_topplate(t). For now, I used a scissor mechanism, with two bars (size L) crossed in a X-shape, almost horizontal at the initial moment (angle theta between one bar and horizontal = 2°), at theta=60° at the final moment.

I am looking for the right actuator for such kind of mechanism. I found a few options, but each have drawbacks:

• horizontal effort F' between 2 bars (usually found in laboratory scissor jacks with a rotating screw): -- Required effort is extremely high when bars are almost horizontal (F'=F/tan(theta)), so I need to find a linear actuator with a super high maximum force (so a super high price), which would only be "used" at the initial moment. --> The inverse mathematical relationship exists between displacements. A 1mm-move from the horizontal actuator would move the top plate by 1mm/tan(2°). So I fear that if I need a millimetric vertical precision for the top plate at the beginning of the movement, I would need a 1mm*tan(2°) precision by the linear actuator, which would increase the actuator cost.

• inclined effort F' between one bar (at a certain height) and base plate: --> Required effort is not constant, and especially very high at the initial moment. Quite the same problem.

• torque between one bar and base plate: --> Required torque is quite high at the initial moment (C'=FLcos(theta)).

• vertical effort between top plate and base plate: --> Looks perfect because effort is constant (F'=F). But there is limited space between plates at the initial moment (z_topplate(0)-z_baseplate(0)) and I need to lift the top plate from z_topplate(0) to z_topplate(tf) knowing that z_topplate(tf)-z_topplate(0) > 4*(z_topplate(0)-z_baseplate). So how can I lift more than the retracted size of the actuator (which needs to fit between plates)? Telescopic actuators, with more than 2 stages, are typically pneumatic or hydraulic, and I would prefer to use only electric motors. --> I thought about rigid chain vertical actuators, but it's extremely expensive.

• vertical effort between bar (at a certain height, for instance one eigth of bar) and base plate --> Looks perfect because effort is constant (F'=8*F). But, my problem is that if there is a 1mm-inaccuracy in the actuator position, that would mean 8mm inaccuracy for the top plate. So it would require highly precise vertical actuator if I need millimetric precision for the top plate.

Is there other mechanism that would fit between the two plates and require a (almost?) constant effort? (or at least, not too high at the initial moment)