Flexible Follower Response of a Translating Cam with Four Different Profiles for Rise-Dwell-Fall-Dwell motion
The flexible follower response of a translating cam with four different profiles for rise-dwell-fall-dwell (RDFD) motion is investigated. The cycloidal displacement motion, the modified sinusoidal acceleration motion, the modified trapezoidal acceleration motion, and the 3-4-5 polynomial motion are employed to describe the rise and the fall motions of the follower and the associated four kinds of cam profiles are studied. Since the follower flexibility is considered, the contact point of the roller and the cam is an unknown. Two geometric constraints formulated to restrain the unknown position are substituted into Hamilton’s principle with Lagrange multipliers. Applying the assumed mode method, one can obtain the governing equations of motion as non-linear differential-algebraic equations. The equations are solved using Runge-Kutta method. Then, the responses of the flexible follower undergoing the four different motions are investigated in time domain and in frequency domain. Keywords—translating cam, flexible follower, rise-dwell-falldwell, response
The vibration of disc cam mechanism
Abstract In this paper, the longitudinal vibrations of a follower which is the linear active component of a cam mechanism is studied as if it has a constant cross section. The basic Bernoulli method is applied to solve the partial differential equation which is supplied by taking the viscous damping factor into consideration and by adding a new term. For the first time, in addition to the viscous damping, in this investigation, the internal damping term has been imposed to the motion of the follower. The resultant integration constants are determined by using the boundary conditions, and the eigen frequencies are calculated. As a result, two different families of eigen frequencies are remained. The results are formed as computer graphics to be easily understandable.
A class of truncated sequential nonparametric tests with constant boundaries: design and performance
Abstract We consider the design and performance of a class of truncated sequential nonparametric tests with two constant thresholds for testing a shift in the alternative. The design involves calculation of the thresholds and the truncation point. We propose to use the Asymptotic Relative Efficiency (ARE) for this. First, the ARE of these tests with respect to the corresponding fixed-sample-size (FSS) tests is obtained as a function of the ratio of the two thresholds, as well as the error probabilities. Given the desired error probabilities, the threshold ratio can be optimally chosen. Then, with this optimal choice and other associated constants, the thresholds can be calculated. Results show that the asymptotic performances of these test are significantly better than the corresponding FSS nonparametric tests. A sequential sign test is used as an example to demonstrate the design procedure and to show non-asymptotic performance, which agrees well with asymptotic results.