Apparatus and method for determining the inertia matrix of a rigid body
First Claim
1. An apparatus for determining the inertia matrix of a rigid club head comprisinga pair of spaced apart supports;
- a balance beam mounted on and across said supports for pivoting about an axis extending longitudinally of said beam;
means removably secured to said beam to receive a known weight thereon;
a first adapter for mounting a club head on said balance beam for selectively balancing the club head about a Z-axis extending along a centerline of a hosel of the club head relative to said known weight with a face of the club head disposed horizontally to determine an x-coordinate of the center of mass of the club head and with the face of the club head disposed vertically to determine a y-coordinate of said center of mass; and
a second adapter for mounting the club head on said beam with said Z-axis perpendicular to said beam for balancing the club head about an X-axis parallel to the face of the club head to determine a Z-coordinate of the center of mass.
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Abstract
The experimental determination of the moments of inertia of a rigid body such as a golf-club head about each of three mutually perpendicular axes is described. The club head is suspended so as to swing as a pendulum about an axis that is parallel to each of the axes of interest and the moments of inertia are calculated from the periods of oscillation and physical properties of the body. The products of inertia must be calculated from the moments of inertia in multiple axis systems. Once the inertia matrix is complete, the associated ellipsoid of inertia displays the inertial properties of the rigid body without reference to a specific coordinate system. The inertia ellipsoids of two golf-club heads are determined and compared to demonstrate the procedure.
35 Citations
6 Claims
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1. An apparatus for determining the inertia matrix of a rigid club head comprising
a pair of spaced apart supports; -
a balance beam mounted on and across said supports for pivoting about an axis extending longitudinally of said beam; means removably secured to said beam to receive a known weight thereon; a first adapter for mounting a club head on said balance beam for selectively balancing the club head about a Z-axis extending along a centerline of a hosel of the club head relative to said known weight with a face of the club head disposed horizontally to determine an x-coordinate of the center of mass of the club head and with the face of the club head disposed vertically to determine a y-coordinate of said center of mass; and a second adapter for mounting the club head on said beam with said Z-axis perpendicular to said beam for balancing the club head about an X-axis parallel to the face of the club head to determine a Z-coordinate of the center of mass. - View Dependent Claims (2, 4)
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3. An apparatus for determining the inertia matrix of a rigid club head comprising
a pair of spaced apart supports; -
a balance beam mounted on and across said supports for pivoting about an axis extending longitudinally of said beam; means connected to said beam to determine a period of oscillation of said beam with a club head thereon; a first adapter for mounting a club head on said balance beam for oscillating the club head about a Z-axis extending along a centerline of a hosel of the club head parallel to said balance beam to determine the moment of inertia IZZ about said Z-axis; and a second adapter for mounting the club head on said beam with said Z-axis extending vertically and perpendicularly of said beam to obtain moments of inertia IXX, IYY about the respective X and Y axes of the club head. - View Dependent Claims (5)
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6. A method of determining the inertia matrix of a rigid body comprising the steps of
establishing a reference coordinate system for the body having three mutually perpendicular axes (X, Y, Z) balancing said body about a reference axis parallel to and in a common vertical plane with one of said axes (Z) with the remaining axes (X, Y) in a vertical plane to obtain a first coordinate of the center of mass of said body; -
balancing said body about said one axis (Z) with said remaining axes (X, Y) in a horizontal plane to obtain a second coordinate of said center of mass; balancing said body about said reference axis with said one axis perpendicular to said reference axis to obtain a third coordinate of said center of mass; thereafter determining a moment of inertia of said body about each of said axes (X, Y, Z) mathematically calculating a moment of inertia (Ixx, Iyy, Izz) of said body about each axis through said center of mass parallel to said three axes using the parallel-axis theorem
space="preserve" listing-type="equation">I.sub.kk =I.sub.KK +md.sup.2wherein IKK is the moment of inertia about an axis of rotation kk, m is the mass of the body, d is the distance of the center of mass of the body from the kk axis and IKK is the moment of inertia through the center of mass; thereafter determining the products of inertia (IXY, IXZ, IYZ) with respect to each said axis passing through said center of mass from said moments of inertia about each said axis and the moments of inertia calculated with respect to a second reference coordinate system (X'"'"'Y'"'"'Z'"'"') at said center of mass; obtaining an inertia matrix [I] for said body wherein ##EQU14## calculating three principal moments of inertia of said body from said inertia matrix and principal-axis direction cosines with respect to said axes of said body; and graphically representing said three principal moments of inertia about arbitrary axes with said principal axes being along the axes of an ellipsoid to form an inertia ellipsoid.
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Specification