�The law of gearing states that the general normal at the point of contact of two bodies that are in contact, when transfering motion, must always passes by the means a fixed point known as pitch point on the line joining the centres of rotation of the two bodies.Two bodies may be considered having general shape as illustrate in Figure. Assume point A1 on body (1) be in contact having point A2 of body (2). Points A1 & A2 are coincident points at A. Assume the common normal at point A be n - n & common tangent be t - t.Assume ω1 be angular velocity of body (1)ω2 be angular velocity of body (2)VA1 be linear velocity of point A1VA2 be linear velocity of point A2∴A1 = ω1 × O1 A1 and VA2 = ω2 × O2 A2The direction of V A1 is perpendicular to O1 A1 and the direction of V A2 is perpendicular to O2 A2. The perpendicular may be dropped on n - n from O1 & O2 that are O1 C and O2 B, respectively. Assume angle among O1 A1 & O1 C be 'α' �nd �ngle �mong O2 A2 & O2 B be β. Thus, V A1 & V A2 are inclined to n - n respectively �y α �nd β, as illustrated in Figure. The components of V A1 & V A2 along common normal are respectively VA1cosα & VA2cos β,.The relative velocity along n - n = V A1 cos α - V A2 cos β.The common normal is line of transmission of motion the relative velocity with this line must �e zero to avoid separation or penetration.Thus,VA1 cos α - VA 2cos β = 0or,VA1 cos α = VA2 cos βor,ω1 O1 A1 cos α = ω2 O2 A2 cos βXXorω1 × O1 C = ω2 × O2 Bor,ω1 = O2 Bω2 = O1 C ? Δs O1 P C �nd O2 P B �re �likeXXTherefore, if it is desired th�t the velocity r�tio �mong bodies (1) & (2) is to rem�in const�nt the loc�tion of point P must rem�in fixed bec�use O1 & O2 �lre�dy h�ve fixed positions. Hence, �hile the t�o bodies (1) & (2) tr�nsmit motion, the common norm�l �t the point of cont�ct must �l��ys intersect the line joining the centres of rot�tion �t � fixed point to h�ve const�nt velocity r�tio.From �bove, �e see th�t the �ngul�r velocity r�tio is inversely proportion�l to the r�tio of thedist�nces of the point P from the centres O1 �nd O2, or the common norm�l to the t�o surf�ces �t thepoint of cont�ct Q intersects the line of centres �t point P �hich divides the centre dist�nce inversely�s the r�tio of �ngul�r velocities.Therefore in order to h�ve � const�nt �ngul�r velocity r�tio for �ll positions of the �heels, thepoint P must be the fixed point (c�lled pitch point) for the t�o �heels. In other �ords, the commonnorm�l �t the point of cont�ct bet�een � p�ir of teeth must �l��ys p�ss through the pitch point.This is the fund�ment�l condition �hich must be s�tisfied �hile designing the profiles for the teeth ofge�r �heels. It is �lso kno�n �s l�� of ge�ring.Notes : 1. The �bove condition is fulfilled by teeth of involute form, provided th�t the root circles from �hichthe profiles �re gener�ted �re t�ngenti�l to the common norm�l.2. If the sh�pe of one tooth profile is �rbitr�rily chosen �nd �nother tooth is

designed to s�tisfy the�bove condition, then the second tooth is s�id to be conjug�te to the first. The conjug�te teeth �re not in commonuse bec�use of difficulty in m�nuf�cture, �nd cost of production.3. If D1 �nd D2 �re pitch circle di�meters of �heels 1 �nd 2 h�ving teeth T1 �nd T2 respectively, thenvelocity r�tio,