I want to know all of the maths concerning this scissor mechanism!

[Maglatron]

any chance you could use the numbers provided to explain what you mean please Mr Alec_t
could I use the mean slope at max radius to give the max torque needed?

 

[Alec_t]

Wt (weight) is the force exerted by gravity acting on the mass. Weight = mass x gravity = 0.275 Kg.

could I use the mean slope at max radius to give the max torque needed?

Yes, since without complicating things further you will only get an approximation anyway, given all the gearing and unknowns (scissor weight, friction etc).
Mean slope = (Rmax-Rmin)/(Rmean x pi).
Another way of calculating theoretical torque in a lossless system would be to consider the work done in raising the weight Wt a height h. That work equals the torque T x pi radians (half a rev of the two-lobe cam).

 

[Maglatron]

average radius of (0.324m + 0.45m)/2 = 0.342
slope is (Rmax-Rmin)/(π x Ravg). (0.45 - 0.342)/(π * 0.342) = 0.1005189114
weight = 0.2753233775kg
lateral force = 0.2753233775kg * 0.1005189114 = 0.0276752062N
MAX Torque = 0.0276752062N * 0.45m = 0.01245384279Nm
correct??

 

[Alec_t]

The average radius value is wrong, so are the slope and lateral force values as a result.
You also forgot the 9.81 factor if you want the lateral force in Newtons.

 

[Maglatron]

ok
average radius of (0.324m + 0.45m)/2 = 0.396
slope is (Rmax-Rmin)/(π x Ravg). (0.45 - 0.342)/(π * 0.396) = 0.08681178714
weight * 9.80665 = 2.7N
lateral force = 2.7N * 0.08681178714 = 0.2343918253N
MAX Torque = 0.2343918253N * 0.45m = 0.1054763214Nm
correct??

 

[Alec_t]

Still wrong. You used the value 0.342 instead of 0.324.

 

[Maglatron]

oh ok
average radius of (0.324m + 0.45m)/2 = 0.387
slope is (Rmax-Rmin)/(π x Ravg). (0.45 - 0.324)/(π * 0.387) = 0.1036357769
weight * 9.80665 = 2.7N
lateral force = 2.7N * 0.1036357769 = 0.2798165976
MAX Torque = 0.2343918253N * 0.45m = 0.1259174689Nm
correct??

 

[Alec_t]

Ok.

 

[Maglatron]

 

[Alec_t]

Just spotted another error. In post #187, lateral force is right but max torque uses the wrong lateral force.

 

[Maglatron]

erm ok can you explain please, thanks

 

[Alec_t]

You have 0.279.... in the penultimate line but used 0.234..... in the last line.

 

[Maglatron]

oh shizer
ok
average radius of (0.324m + 0.45m)/2 = 0.387
slope is (Rmax-Rmin)/(π x Ravg). (0.45 - 0.324)/(π * 0.387) = 0.1036357769
weight * 9.80665 = 2.7N
lateral force = 2.7N * 0.1036357769 = 0.2798165976N
MAX Torque = 0.2798165976N * 0.45m = 0.1259174689Nm
correct?? I used the correct number for the calculation but because of copy paste, I forgotten to alter the Lf value in the MAX Torque equation! thanks

 

[Alec_t]

 

[Maglatron]

so this is an important question the block at height 1.26m has potential energy of (1.256637061m * 9.80665m/s^2 * 0.2753233775kg) = 3.392920065J
but the torque * radian (the rotational equivalent to F * d) eg work
0.1259174689Nm * π = 0.3958147464J
how is this?

 

[Maglatron]

so my laptop is fully f***** and won't charge so when the battery dies probably won't be on for at least 3 weeks. Two weeks before I can order and a a few days for postage. So if you can answer this before it does die I'd be well happy

 

[Alec_t]

I don't think you need that g factor in the potential energy calculation, since it is inherent in weight (as distinct from mass).

 

[Maglatron]

hmm this is why I like decimals without the g factor it equals 0.3459815599J of PE and I argue that you do need the 9.80665 because mgh is potential energy
mass in kg, g 9.80665m/s^2, h 1.2566m

 

[Alec_t]

because mgh is potential energy

mg = weight. So PE =weight x h.

 

[Maglatron]

mgh in Physics: Refers to the potential energy (PE) of an object in the context of gravitational potential energy. The formula is:

PE=mgh
where:

• m is the mass of the object,
• g is the acceleration due to gravity,
• h is the height above the reference point.

in the context of the gravitational potential energy formula (PE=mgh), the mass (m) is measured in kilograms (kg). Here's a breakdown of the units used in this formula:

• m (mass): measured in kilograms (kg)
• g (acceleration due to gravity): measured in meters per second squared (m/s²)
• h (height): measured in meters (m)

When you multiply these together, the resulting potential energy (PE) is measured in joules (J), which is the standard unit of energy in the International System of Units (SI).
weight force is measured in Newtons, and NOT kg, weight force is the product of the mass and the g factor, and gives newtons. The 2.7N is a product of the mass which is 0.2753233775kg * 9.80665m/s^2 (mg)

which in my case is 2.7N
2.7N * 1.256637061m = 3.392920062J