Please see the attached file for the fully formatted problem(s).

My problem is explained more in my attachment, but briefly, I require some form of equation or graph to calculate where the pivot points within a seven point hinge system need to be in order for the rotating edge to rotate around a origin.

The question is in regard to the hinge system.
I require the hinge, when expanded, to rotate around the origin with 0 tolerance.
THE HINGE
What I know
Through pure trial and error, involving no mathematical formulas or graphs, I have
narrowed down where the pivot points, approximately need to be placed so it rotates
around the origin.
I did this by lengthening and shortening distances and angles between points, until I
narrowed the solution down to be within 2mm tolerance.
As can be seen in the picture below, the plate that will be used to bend the material
moves up/out/in/and down while rotating around the origin. I require this plate to have no
tolerance, i.e. not move away from the origin at all. Therefore I believe there must be
some sort of graphs or equations that will dictate exact positions the pivot points within
the hinge need to be.
Bending Edge
Origin
Bending edge shown here at different stages of rotation

A boy and a girl are balanced on a massless seesaw. The boy has a mass of 75 kg and the girl's mass is 50 kg.
If the boy sits 2.0 m from the pivotpoint on one side of the seesaw, where must the girl sit on the other side?

See attached file for diagram.
A uniform rod of mass M = 5.18 kg and length L = 1.20 m can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as seen in the figure attached in a Word doc. The rod is held horizontally and then released. Determine the angular acceleration of the rod at the moment of relea

Please see the attached file for diagram.
A designer wishes to make a clock with a pendulum in the shape of a flat disk. Instead of swinging from the end of a rod, however, the disk is to pivot about a point between its center of mass and its rim.
If the disk has a radius of 15.0 cm and its intended period of oscillation

Please refer to the attachment for the mentioned figures.
1. Three masses, 2.0 kg, 3.0 kg, and 6.0 kg, are located at points (3.0, 0), (6.0, 0), and (-4.0, 0), respectively, in meters from the origin. Where is the center of mass of this system?
2. A dumbbell, Figure below, has a connecting bar of negligible mass. Find the

See the attached file for further question details.
A) What is the equation that results from choosing the pivotpoint to be the point from which the mass hangs (where W acts)?
Express your answer in terms of the unknown quantities T_L and T_R and the known lengths x and L. Recall that counterclockwise torque is positive.

determine whether the given simplex tableau is in final form. if so,find the solution to the associated regular linear programming problem. if not, find the pivot element to be used in the next ileration of the simplex method.
x y z u v w P constant
1/2 0 1/4 1 -1/4 0 0 19/2
1/2 1

On the seesaw shown to the right (see attachment), mass A is 60 kg. mass B is 30 kg, and mass C is 10 kg. Mass A is 1.0m from the pivot. Mass C is 3.0m from the pivot. The see saw is at an angle of 30 degrees from the horizontal. Calculate the torques of mass A and mass C about the pivot. Where you should place mass B in relatio

A thin, uniform 12.0-kg bar that is 2.00 m long rotates uniformly about a pivot at one end, making 5.00 complete revolutions every 3.00 seconds.
What is the kinetic energy of this bar? (Hint: Different points in the bar have different speeds. Break the bar up into infinitesimal segments of mass dm and integrate to add up the