Equipoise assembly

A non-linear torque produced by an offset mass rotating on a shaft is balanced over 360.degree. of revolution by a lever arm mounted to the shaft extending in a direction opposite that of the offset mass and a spring means for generating a constant force in the direction of gravity at the opposite end of the lever arm.

This invention relates to an equipoise assembly that produces a torque 
about an axis that is 180.degree. out of phase with the torque produced by 
an unbalanced appendage rotating about that axis. 
As an antenna or a hinged appendage is deployed, the gravitational torque 
about its rotational axis varies sinusoidally with the angle from 
horizontal. Counter balances are frequently added to null this effect, at 
the expense of increased weight and inertia. Sometimes, this approach 
cannot be tolerated. For example, in the art of testing deployable 
appendages on satellites such as booms and antennas, a device is often 
necessary to off-load gravity and simulate zero G (gravity) environment. 
On some of these systems, a counterbalance would affect the deployment 
dynamics so much as to invalidate the test. An even greater problem for 
testing is when the appendage is required to be deployed while the 
satellite is spinning. In this case, a counterbalance weight cannot be 
used since this would be affected by centripetal forces. 
An alternative approach is to null the gravitational effect with a spring 
driven mechanism that has relatively little mass. Existing designs use 
complicated arrangements of cams, springs, gearing and levers, and only 
act over short distances of rotation. The mass unbalance varies as a 
function of the cosine of the elevation angle. This nonlinear relationship 
results in a mechanism that is generally complex and costly to achieve. It 
is desired to achieve this nonlinear relationship continuously over large 
rotation angles at low cost. 
SUMMARY OF THE INVENTION 
In accordance with one embodiment of the present invention there is 
provided an assembly for balancing a nonlinear torque produced by an 
offset rotating mass on a shaft. The assembly includes a lever arm fixed 
at one end to the shaft extending in a direction opposite the offset 
direction of the offset mass and rotates with the shaft and mass. A 
constant force in the direction of gravity is generated at the opposite 
end of the lever arm. The force being of a magnitude and distance from the 
shaft to counter balance the mass continuously.

DESCRIPTION OF PREFERRED EMBODIMENT 
Referring to FIG. 1 there is illustrated a bar 10 representing a mass 
rotated about a pivot point 11. The center of the mass of the bar 10 is 
represented by the symbol labeled (CG) in the middle of the bar. The mass 
may be an antenna or any hinged appendage where the hinge shaft is 
pointing toward the viewer at pivot point 11. As the antenna or hinged 
appendage is deployed, the force due to gravity remains downward as 
represented by .omega. but the torque changes as a function of angle 
.theta. or T=.omega.cos.theta.. In the generalized case, the pivot axis is 
not horizontal but the net effect is the same. The general formula is 
T=.omega.cos.alpha.cos.theta. where .alpha. is the pivot axis elevation 
angle. However, further discussion will be based on a horizontal pivot 
axis for simplicity. 
Curve A of FIG. 2 illustrates a plot of torque produced by the bar as a 
function of the angle .theta.. At angle .theta.=0 the bar is level on the 
ground and there is maximum torque. At about the .theta.=45.degree. 
position shown the torque has lessened and when the bar is straight up so 
.omega. passes through the pivot point 11 the torque is zero. At 
.omega.=135.degree. the torque is the same as at 45.degree. but is in the 
opposite direction. At 180.degree. the torque is again maximum in the 
opposite direction. At the .theta.=225.degree. the torque is the same 
amount and sign as at 135.degree.. At .theta.=270.degree. the torque is 
zero. At .theta.=315.degree. the torque matches that at 45.degree. in both 
amount and direction. 
In order to completely compensate for the changing torque a device must be 
coupled to the pivot point 11 of the bar 10 that follows curve B of FIG. 2 
so that the torque generated is 180.degree. out of phase with respect to 
curve A. 
In accordance with one embodiment of the present invention this 
compensating torque is provided by the apparatus illustrated in FIGS. 3a, 
3b, 3c and 3d. Referring to the side and end views of FIG. 3a and 3b there 
is shown the bar 301 that may be coupled at flanged end 303 to an antenna 
to be deployed. The opposite end 305 of bar 301 is fixedly mounted by 
coupler 307 to shaft 309. Shaft 309 at the pivot point passes through 
bushing 310. Bushing 310 is in assembly support wall 31. 
The balancing apparatus 315 is coupled to shaft 309. The apparatus includes 
a lever arm 319 having one end 319a fixedly coupled to shaft 309 at end 
309a so that the bar 301, the shaft 309 and arm 319 move as a unitary 
body. The opposite end 319b of lever arm 319 is fixedly coupled via shaft 
321 to a wheel 323. The shaft 321 passes through the lever arm at end 319b 
and the center of wheel 323. The wheel 323 includes, for example, a 
central aperture and ball bearings about the aperture. The shaft 321 is 
fixed to the lever arm 319 and moves with the bar 301, shaft 309 and arm 
319. The shaft 321 passes through the aperture in wheel 323. The wheel 323 
rotates on ball bearings about shaft 321. A constant downward force in the 
direction of arrow 88 is provided by negator springs 340, a sliding 
mechanism 341 and a bar 345. 
Negator springs 340 are mounted on the back side of support wall 31 and are 
fixedly coupled via shaft 343 to a pulley wheel 365. The negator springs 
produce a constant torque in the direction of arrow 349 on the shaft 343 
and pulley wheel 365. A cable 347 is coupled at a point 350 on the 
periphery of the pulley wheel 365 and wraps partially around the periphery 
of the pulley wheel 365. 
The slider mechanism 341 includes a cylindrical shaft 371 which is mounted 
vertically in FIG. 3a and is oriented in a direction perpendicular to the 
shafts 309 and 343 which are parallel to each other. The ends of the shaft 
371 are fixedly mounted using mounts 373 and 375 such that the cylindrical 
bar 371 extends out from the wall 31. A hollow cylindrical slider 360 is 
considerably shorter in length than the shaft 371. The dimension of an 
inner aperature of slider 360 is such that the mechanism 360 slides 
smoothly along the shaft 371. Bushings 372 are located within the hollow 
of slider shaft 360 to accommodate a smooth sliding action along the 
length of shaft 371. The cable 347 is connected at end 365 to this slider 
mechanism 360. A bar 345 shown horizontal in the FIG. 3a extends 
perpendicular to shaft 371 and perpendicular to the shafts 309 and 343. 
This bar 345 is mounted at one end to the slider 360 and extends and makes 
contact with wheel 323. Wheel 323 may be a pulley with a grooved periphery 
and the bar 345 as illustrated is cylindrical and fits into the groove 
about the wheel 323. The negator springs provide a constant force on the 
wheel in the direction of 88 by providing a constant pull on the bar 345 
via the slider 360 and cable 347. 
The position of wheel 323 and the lever arm 319 are arranged with respect 
to the position of bar 301 so as to produce a torque following curve B of 
FIG. 2 that is 180.degree. out of phase with respect to the torque 
presented by the bar 301. 
Referring to FIGS. 4a-4d there is illustrated in schematic form how the 
constant torque provided by negator springs on the wheel 365 produces with 
different shaft positions the compensating and varying torque. The torque 
on wheel 365 produces a steady downward (direction 88) force through the 
center of wheel 323. The dashed lines 301 represent the deployed bar which 
may be the antenna mast. Referring to FIG. 4, when the lever arm 319 and 
wheel 323 are in the positions illustrated in FIGS. 3a and 3b, the bar 301 
is in .theta.=0.degree. position where maximum torque is provided by the 
bar 301 in the counterclockwise direction and maximum torque is applied by 
the assembly 315 in the opposite (clockwise) direction to that produced by 
arm 301. When the arm 301 is rotated into the vertical upward direction 
(.theta.=90.degree.) and the lever arm 319 is rotated to the downward 
position to align with arrow 80, both the center of mass of bar 301 and 
the force through the center of wheel 323 pass through shaft 309 (pivot 
axis) and the torques are both zero. This is represented in FIG. 4b. 
Between the bar 301 positions of FIG. 4a and 4b the torques produced are a 
function of the angle with the assembly 315 matching in opposite sense 
that produced by the bar 301. When the lever arm 319 and bar 301 are 
rotated 180.degree. from the initial position, as in FIG. 4c, the bar 301 
produces maximum clockwise torque and the assembly 315 provides maximum 
counterclockwise torque. 
FIG. 4d illustrates when the bar has been rotated 270.degree. and the lever 
arm has been rotated 270.degree. the torques of each are zero. As seen by 
this illustration in the diagrams, the present invention provides an 
apparatus 315 that matches the torques generated by the deployable bar 301 
for all 360.degree. of revolution. 
The size of the negator springs and the number of springs 340 can be 
adjusted to balance out the torques that are generated by the effect of 
the gravitational forces on the bar or offset mass. In accordance with the 
teachings of the present invention therefore, a torque compensation 
technique is provided for a rotating offset mass through 360.degree. of 
rotation. This type of compensating apparatus in addition to being used to 
provide a zero gravity equivalent in a gravity testing facility can also 
be used for providing counterbalancing during deployment of a cantilevered 
antenna, robotic manipulator, crane, etc.