Consider the following system driven by an angle source, theta_s, applied to a s
ID: 1843409 • Letter: C
Question
Consider the following system driven by an angle source, theta_s, applied to a shaft, k, connected to a gear box where the input gear, Gear 1, has radius r_1 and the output gear, Gear 2, has radius r2. The gear ratio is defined as n = r_2/r_1 such that theta_2 = -1/n theta_1 using the positive right hand notation shown where the gearbox is directly coupled to the load inertia J. The inertia is supported by a bearing, B2, and drives a load, B_2, Complete the following, stating assumptions. a) Draw the system diagram and free body diagrams of all inertias and elements. b) Write the element equations. c) Apply D'Alembert's law to the system to form equation(s) in terms of element torques. d) Combine the equations from b) and c) to form the differential equation describing the dynamics of the system. The equations should be in the preferred form discussed in class (e.g. higher derivatives of appear first followed by lower derivatives on the RHS; forcing terms are on the RHS; inertia terms such as J theta_2 are not multiplied by any other parameters in the theta_ equation). Circle your final answer.Explanation / Answer
D'Alemberts principle also known as the lagrange -d'alembert principle is a statement o the fundemental classes laws of motion. it is named after its discoverer, the french physicist and mathematican jean le rond d'alembert. it is the dynamic analogue to the principle of virtual work for applied forces in a static system and in fact is more general than hamiltions principle, avoiding restriction to holonomic system. a holonomic constraint depends only on the coordinates and time. it does not depend on the coordinates and time. it does not depend on the velocities. if the negative terms in accelerations are recognied as inertial forces,the statement of dalembert's principle becomes the total virtual wprk of the impressed forces plus the intertial work of the impresses forces plus the intertial forces vanishes for reversible displacements