In a ball spline joint which regulates the rotation of a shaft and permits only displacement in an axial direction, many balls are held in a space between an inner spline groove formed in outer circumference of a shaft and an outer spline groove formed in the inner circumference of a support member.
In the case of this joint structure, machining error of the spline grooves causes scatter in the clearance between the balls and spline grooves. As a result, slackness between a shaft and support member easily becomes uneven. However, slackness which is too large or too small reduces the durability of the joint.
The slackness can be quantized by inserting measuring balls with a predetermined diameter smaller than those used in the product and measuring how much the outer spline groove can displace relative to the inner spline groove in a circumferential direction.
It is also known that the slackness of the product can be maintained within a fixed range by varying the diameters of the balls assembled in the spline grooves according to the quantized slackness.
The principle of a measuring apparatus for measuring slackness for this purpose is shown in FIG. 8.
In this figure, spline grooves are respectively formed between an outer circumference of a shaft 56 and inner circumference of a boss 54, a large number of balls being held in these spline grooves.
When the boss 54 is rotated in the forward and backward directions with a predetermined torque, a first measurement point P1 and second measurement point P2 which have been set to rotate with the boss 54 also move. The travel distance A1 of the measurement point P1, and the travel distance A2 of the measurement point P2 are respectively measured by a first gauge 11 and second gauge 12.
The first measurement point P1 and second measurement point P2 are set on a straight line B which intersects with the center line of a spline groove and a center axis O.sub.40 of the shaft 56.
The first measurement point P1 is set at a distance R1 from the center axis O.sub.40, and the second measurement point P2 is set at a distance R2 from the same.
A slackness A0 is computed by the following equation from the distances A1, A2 through which these measurement points P1, P2 displace due to the rotation of the boss 54. ##EQU1## where, R0=diameter of shaft.
In this measurement method, the first measurement point P1 and second measurement point P2 are set on the same radial line. Therefore, as shown in FIG. 9, when for example the measurement value A1 is obtained as a value A1' having a certain positive error, the computed value A0' of the slackness is computed to be much larger than the actual value A0. As a result, the measurement error in the slackness A0 is too large.