# US 4,393,690 A · Force balancing techniques for complex cyclically moving planar linkages

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- Number: US 4,393,690 A
- Document ID: US4393690A
- Status: Granted
- Kind: A
- Application number: 06/262,826
- Filed: 1981-05-12
- Granted: 1983-07-19
- Earliest claimed: 1981-05-12
- Assignees: Research Foundation of the City University of New York
- Inventors: Gerard G. Lowen; Stephen J. Tricamo
- Web page: https://patentgrep.com/patent/US4393690A

## CPC

- F16F 15/22: Compensation of inertia forces {(suppression of vibrations of rotating systems by favourable grouping or relative arrangements of the moving members of the system or systems F16F15/20, counterweights F16F15/28; correcting-weights for balancing rotating bodies F16F15/32)}
- F16F: SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION

## Abstract

This invention provides a technique for reducing shaking forces in n-bar type planar linkages. Thus a linkage is reciprocated and the shaking forces determined in two different coordinates of the plane of operation. With information on crank arms, operating position and velocity of the reciprocating linkage, the relationship F.sub.s =Ma furnishes balancing equations which may be solved by calculation using detected readings at a plurality of linkage positions to give the masses and positions of corrective balancing members for reducing the shaking forces. Instrumentation primarily comprises a force platform such as a piezoelectric device upon which the linkage is mounted for cyclic reciprocation to produce dynamic force signals along a set of two coordinates in the plane of operation at various linkage positions. Appropriate data processing equipment then calculates from the balancing equations the corrective masses and their positions for reducing the shaking forces. The calculation can be automatically done in computing equipment, and the shaking forces along the coordinates can be displayed on an oscilloscope for analysis and indication of the balance.

## Claims

### Claim 1

The method of fully force balancing cyclically moving planar n-bar linkages to reduce residual shaking forces comprising the steps of,
cyclically moving the planar linkage through its movement cycle,
determining during the cyclic movement in the plane of movement the shaking forces (F.sub.s) along a set of two coordinates, such as the x and y axes, for a plurality of angular sensing positions in the movement cycle,
determining the angular position and angular velocity of the input link at said plurality of positions to thereby provide a plurality of sets of data,
and establishing from the plurality of sets of data determining the shaking forces at the plurality of sensing positions with the help of the balancing equations the required corrective mass and location of counterbalance structure for reducing the shaking forces F.sub.s of both fundamental frequencies and harmonics of the cyclic movement.

### Claim 2 (depends on 1)

The method defined in claim 1 including the steps of,
mounting the planar linkage for cyclic movement upon a force platform, and
establishing the shaking force coordinate components by measuring in respective coordinates the forces introduced to the platform by the reciprocating linkage.

### Claim 3 (depends on 1)

The method defined in claim 1 including the step of determining the angular position of the linkage in its cycle by means of an angular encoder moving cyclically with said linkage.

### Claim 4 (depends on 1)

The method defined in claim 1 including the step of coupling variable speed motor means for cyclically driving and thereby reciprocating the linkage at a predetermined speed.

### Claim 5 (depends on 4)

The method defined in claim 4 including the steps of,
cyclically rotating two rotary members connected by a bar link in respective bearing assemblies,
and mounting the two bearing assemblies on a common force platform from which said shaking forces F.sub.s in the two coordinates are derived.

### Claim 6 (depends on 1)

The method defined in claim 1 including the steps of determining the velocity of the angular movement and differentiating the determined velocity to derive the angular acceleration.

### Claim 7 (depends on 1)

The method defined in claim 1 including the step of establishing the shaking forces at variable cyclic reciprocation speeds.

### Claim 8 (depends on 1)

The method defined in claim 1 including the step of visually displaying the shaking force F.sub.s on a monitor.

### Claim 9 (depends on 1)

The method defined in claim 1 including the step of determining the location, direction and distance from a reference point of corrective counterbalance masses.

### Claim 10 (depends on 1)

The method defined in claim 1 including the step of mounting the linkage on a force platform and reciprocating the linkage to determine the shaking forces by measurement of forces in said platform.

### Claim 11 (depends on 10)

The method defined in claim 10 including the more detailed step of mounting the linkage on the force platform by means of bearing support means disposed perpendicular to at least one rotation axis position in the linkage plane.

### Claim 12 (depends on 11)

The method defined in claim 11 including the step of providing said bearing support at two locations, namely at force input and force output cranking positions on the linkage.

### Claim 13 (depends on 10)

The method defined in claim 10 including the more detailed steps of mounting the linkage on a single piezoelectric force platform and determining the shaking forces by piezoelectric signals induced in two coordinates in the platform disposed in the plane of movement of the linkage.

### Claim 14

Apparatus for dynamic analysis of the shaking forces of cylically moving planar linkages, comprising in combination, means for moving the linkages over a cyclic movement pattern, detection means for determining cyclic shaking forces in the plane of the linkage at a plurality of points in the movement pattern, and computation means for determining from the shaking forces and the movement pattern characteristics of balancing masses to modify the linkage mass for reducing the shaking forces of fundamental and harmonic frequencies of the cyclic frequency.

### Claim 15 (depends on 14)

Apparatus as defined in claim 14 including means for determining the magnitudes of the balancing masses required for substantially reducing the shaking forces.

### Claim 16 (depends on 14)

Apparatus as defined in claim 14 wherein the means for moving the linkages comprises a variable speed motor.

### Claim 17 (depends on 14)

Apparatus as defined in claim 14 wherein the detection means for determining the shaking forces comprises a force platform upon which the linkage is supported, with means on the force platform indicating forces in two different coordinates in the plane of the linkage.

### Claim 18 (depends on 14)

Apparatus as defined in claim 14 wherein the computation means comprises oscilloscope means displaying visually the shaking force amplitude on one coordinate and the position of the linkage in the cyclic movement pattern another coordinate.

### Claim 19 (depends on 14)

Apparatus as defined in claim 14 including computation means for indicating the positioning of the balancing masses.

### Claim 20 (depends on 14)

Apparatus as defined in claim 14 including means deriving the magnitude of the balancing masses required to substantially reduce shaking forces.

### Claim 21 (depends on 14)

Apparatus as defined in claim 14 including further detection means determining the angular velocity of the input link, wherein the computation means comprises means establishing from the balancing equations the magnitudes of the masses for substantially reducing the shaking force, wherein the value of F.sub.s is sensed by said detection means coupled to the linkage and the means of computing the angular acceleration by differentiating the detected angular velocity.

### Claim 22 (depends on 14)

Apparatus as defined in claim 14 including motor driving means and a motor disconnect clutch in said means for moving the linkages, and sampling means for periodically disconnecting the clutch while activating said sampling means to detect the shaking forces thereby to isolate any motor shaking forces from the detected shaking forces.

### Claim 23 (depends on 14)

Apparatus as defined in claim 14 wherein the detection means comprises a force block with detection devices thereon, and bearing means is affixed to the force block for moving said linkage through its cyclic cranking pattern and thereby transmitting the shaking forces to said detection devices.

### Claim 24 (depends on 14)

Apparatus as defined in claim 14 wherein the means moving the linkage is provided with means for indicating the position of the linkage in the movement cycle.

### Claim 25 (depends on 14)

Apparatus as defined in claim 14 wherein the means moving the linkage is provided with means indicating the movement velocity.

### Claim 26

The method of analysis of the shaking forces in linkages with all components reciprocating in a plane, comprising the steps of,
providing a mechanism reciprocating the linkage,
detecting the shaking forces in the reciprocating linkage in said plane at a plurality of the mechanism positions in the reciprocation cycle,
and displaying from the detected shaking forces and the linkage reciprocation data representative of the shaking forces at a plurality of positions in the reciprocation cycle.

### Claim 27 (depends on 26)

The method of claim 26 wherein the shaking forces are detected in two coordinate directions in said plane, and the reciprocation data in each coordinate is displayed.

### Claim 28

The method of determining corrective masses and mass positions for reducing shaking forces in linkages with all components reciprocating in a plane, comprising the steps of,
reciprocating the linkage,
detecting in a pair of coordinate directions in said plane the shaking forces for a plurality of linkage positions, and
calculating from the balancing equations the corrective masses and positions for corrective changes reducing the shaking forces.

### Claim 29

Apparatus for dynamic analysis of the shaking forces of planar linkages, comprising in combination,
means moving the linkages over a cyclic movement pattern,
detection means for determining the shaking forces and angular velocity in the plane of the linkage at a plurality of points in the cyclic movement pattern of the linkages to derive a plurality of sets of data,
and means for processing the detected plurality of sets of data for analysis for the shaking forces to derive corrective masses and positions for reducing shaking at the cyclic frequency and its harmonics.

### Claim 30 (depends on 29)

The apparatus defined in claim 29 wherein the means for processing the shaking forces comprises a visual display device for displaying the detected shaking force magnitudes at said plurality of cyclic movement positions.

### Claim 31 (depends on 30)

The apparatus as defined in claim 30 wherein the visual display device comprises an oscilloscope, the detection means provides a dynamic reading throughout the cyclic movement pattern, and the oscilloscope display provides a trace representative of the entire cyclic movement pattern.

### Claim 32 (depends on 29)

The apparatus as defined in claim 29 wherein the means for processing the shaking forces comprises a calculator programmed for computing from the detected shaking forces the mass and position of corrective members for reducing shaking forces.