Embedded Files
Contents
Contents
Course Information
Course Information
Date I took this class: Fall 2008
Teacher: Jose Granda
Teacher's site: http://gaia.ecs.csus.edu/~grandajj
Grade earned: A
Book used: Vector Mechanics for Engineers: Dynamics
By Ferdinand Pierre Beer
Information About Teacher
Information About Teacher
Professor Granda is, overall, a teacher with a unique teaching style.
Granda is involved in NASA and has access to information on various exciting projects and missions.
Granda is always willing to take time to help individual students.
Granda assigns homework on a bi-monthly basis from the text. Those who do the homework can get good grades.
Granda's tests are taken directly from the text book. All those who are able to do the homework should be able to complete the tests.
The Vector Mechanics text is required and is used in class. Virtually all homework is assigned from this text.
Virtual Modeling Presentations
Virtual Modeling Presentations
Working Model
Chapter 15 Presentations
Problem #57 - The Rotating Disk Problem.
Nastran4D
Chapter 15 Presentations
Problem #204 - The Two Rotating Rods Problem.
Video
Rube Goldberg machine by Drew
Final Project
Final Project
Synopsis
The goal of this project is to recreate the space shuttle arm and model its motions in a 2D and 3D environment. Once modeled the motions of the arm will be analyzed. In addition to motion analysis, a stress analysis will also be conducted.
Project Report
The Shuttle Arm report
Project Presentation
The space Shuttle Arm presentation
Solving Dynamics Problems
Solving Dynamics Problems
Aaron's Method
In dynamics we mainly deal with velocities and accelerations. In fact, almost all dynamics problems involve solving for velocities and/or accelerations of points, either as the result or as an intermediate step. My method makes solving for velocities and accelerations very easy. The only thing necessary to solve most dynamics problems is to find the velocity and/or acceleration of one point in terms of another. Its as simple as that. With this simple principle there are only three equations needed to solve nearly all dynamics problems. Note: A, B, and C are points on a non-rigid body, v is the velocity vector, a is the acceleration vector, and w is either v or a.
v_A/B = v_A'/B + (v_A/B)_rot ... (eqn 1)
a_A/B = a_A'/B + (a_A/B)_rot ... (eqn 2)
w_A/C = w_A/B + w_B/C ... (eqn 3)
Written form:
In Words
(eqn 1): The velocity of A with respect to B is equal to the velocity of point A (on the rigid body!) with respect to B plus the velocity of A with respect to B in the rotating, rot, reference frame.
(eqn 2): The acceleration of A with respect to B is equal to the acceleration of point A (on the rigid body!) with respect to B plus the acceleration of A with respect to B in the rotating, rot, reference frame.
(eqn 3): The velocity (or acceleration) of A with respect to C is equal to the velocity (or acceleration) of point A with respect to B plus the velocity (or acceleration) of B with respect to C.
If you are in dynamics then the rotating reference frame should not be used yet. If you are not dealing with rotating reference frames the first two equations simplify to the following:
v_A/B = v_A/B ... (eqn 4)
a_A/B = a_A/B ... (eqn 5)
Written form:
The two equations you should be very familiar with already are below. Note, "-->" represents an arrow, "x" represents the cross product, r_B-->A is the position vector from B to A, omega is the angular velocity vector, and alpha is the angular acceleration vector.
v_A/B = omega_AB x r_B-->A ... (eqn 6)
a_A/B = (a_A/B)_tangential + (a_A/B)_normal = alpha_A/B x r_B-->A - omega^2*r_B-->A ... (eqn 7)
Written form:
With the knowledge of equations 6 and 7 already drilled into you, all you need to learn are equations 1, 2, and 3 and you will be ready to solve almost all dynamics problems!
Below are examples of ways I have solved dynamics problems using the problem-solving method I created.
Example Problem - Rods in motion, rigid body problem, rotation component not needed.
Ch. 15 Problem #153 - Bars rotating causing a collar to translate.
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