This paper presents a method for defining the relationship between the angular coordinates of N-lobe noncircular gear wheels using Bézier and B-spline nonparametric curves. After designing the displacement law, conjugate pitch curves are obtained using an analytical method that takes the driver angular coordinate as an input variable. With N-lobe noncircular gears, the number of speed cycles per revolution can be increased. In addition, N-lobe noncircular gears are well balanced because they rotate around their geometric center. Bézier nonparametric curves and B-spline nonparametric curves are used to obtain the displacement laws of an N-lobe noncircular gear. Using these functions, an N-lobe noncircular gear that satisfies a given relationship between the rotation angles of the driving and driven wheels can be designed or a given transmission ratio can be obtained.

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This article examines new tutoring evaluation methods to be adopted in the course, Machine Theory, in the Escola Tècnica Superior d'Enginyeria Industrial de Barcelona (ETSEIB, Universitat Politècnica de Catalunya). These new methods have been developed in order to facilitate teaching staff work and include students in the evaluation process. Machine Theory is a required course with a large number of students. These students are divided into groups of three, and required to carry out a supervised work constituting 20% of their final mark. These new evaluation methods were proposed in response to the significant increase of students in spring semester of 2010-2011, and were pilot tested during fall semester of academic year 2011-2012, in the previous Industrial Engineering degree program. Pilot test results were highly satisfactory for students and teachers, alike, and met proposed educational objectives. For this reason, the new evaluation methodology was adopted in spring semester of 2011-2012, in the current bachelor's degree program in Industrial Technology (Grau en Enginyeria en Tecnologies Industrials, GETI), where it has also achieved highly satisfactory results.

The base circle of a circular gear is concentric with the pitch circle and tangent to the action line. However, in a noncircular gear the base curve is not known a priori and not easy to determine. In this study, the base curves of noncircular gear wheels are obtained as the geometrical locus of the singular points on the involute tooth profile. Singular points—points from which a second involute branch begins to form on the tooth profile—restrict the allowable tooth height and allow the minimum number of teeth required to be estimated. We discuss the influence of the curvature radius of the pitch curve on the allowable tooth height and present an example to illustrate the proposed method.

Abstract. The mechanisms of one degree of freedom can be dynamically analysed by setting out a single differential equation of motion which variable is the generalized coordinate selected as independent. In front of the use of a set of generalized dependent coordinates to describe the system, the method exposed in this work has the advantage of working with a single variable but leads to complex analytical expressions for the coefficients of the differential equation, even in simple mechanisms. The theoretical approach, in this paper, is developed from Eksergian's method and Lagrange's equations. The equation of motion is written by means of a set of parameters -reduced parameters -that characterize the dynamic behaviour of the system. These parameters are function of the independent coordinate chosen and its derivative and can be obtained numerically by direct calculus or by means of a kinetostatic analysis, as is proposed. Two cases of study of the method are presented. The first example shows the study of pedalling a stationary bicycle used in a rehabilitation process. The second one shows the analysis of a single dwell bar mechanism which is driven by an electric motor.