C A PRACTICAL TREATISE ON THE TEETH OF WHEELS With the Theory and the use of ROBINSON'S ODONTOGRAPH. BY S. W. ROBINSON, Professor of Mechanical Engineering, ILLINOIS INDUSTRIAL UNIVERSITY. D. VAN NOSTRAND, PUBLISHER, 23 MURRAY AND 27 WARREN STREET. 1876. PREFACE. The present little volume, reprinted from the pages of VAN NOSTRAND'S MAGAZINE, has resulted from an effort to bring before the mechanical public improved facilities for obtaining correct gearing. Correct gear teeth are essential for the econ omic transmission of power, as well as extremely desirable for avoiding needless rattling. Many of the cast gears introduced into mills and factories may properly be termed rattling machines, and simply because the designer had too vague a conception of the theory of gearing, or because he sought to avoid the trouble of laying them out. If this manual, and the odontograph, shall contribute toward relieving these inconveniences, the object sought, when the instrument was devised, and an effort made to present it in convenient form for use, will be realized. ILLINOIS INDUSTRIAL UNIVERSITY, S. W. R. July, 1876. PART I. ON THE THEORY OF GEAR TEETH. AND ADAPTATION OF PARTICULAR FORMS THOUGH the curves which may be employed for the outlines of mathematically correct gear teeth are infinite in number, varying greatly in external appearance, yet all of them must conform with one general principle, viz.: tooth curves must transmit, from one shaft to the other, the same motion as would the pitch lines when acting by simple rolling contact. This truth is, in reality, axiomatic; and for the present purpose needs no discussion or comment. It forms the basis of the present investigation, the object of which is to show how the |