UCLA, MAE 102

Excerpt: ... Examples from Chapter 6: Plane Kinetics of Rigid Bodies : Chatterjee Taking moment about P, we have Note: Steady State Problem. No rotation, Deflection angle is maintained at 15 during motion Examples from Chapter 6: Plane Kinetics of Rigid Bodies : Chatterjee Problem 6/15 Continued. Examples from Chapter 6: Plane Kinetics of Rigid Bodies : Chatterjee Examples from Chapter 6: Plane Kinetics of Rigid Bodies : Chatterjee Examples from Chapter 6: Plane Kinetics of Rigid Bodies : Chatterjee Examples from Chapter 6: Plane Kinetics of Rigid Bodies : Chatterjee Examples from Chapter 6: Plane Kinetics of Rigid Bodies : Chatterjee Examples from Chapter 6: Plane Kinetics of Rigid Bodies : Chatterjee Equations of Motion: Examples from Chapter 6: Plane Kinetics of Rigid Bodies : Chatterjee Examples from Chapter 6: Plane Kinetics of Rigid Bodies : Chatterjee Examples from Chapter 6: Plane Kinetics of Rigid Bodies : Chatterjee Examples from 4th Edition Examples from Chapter 6: ...

Wisconsin, ENGR 542

Excerpt: ... EP/EMA 542 Advanced Dynamics Lecture #14: Rigid Bodies 2007 M.S. Allen 1 Reminders/Announcements Homework #4 due Wed, Oct. 10th Project Sketch Due. Oct. 12th Exam #1 on Monday Oct. 15th! 2007 M.S. Allen 2 1 Rigid Body Body Fixed Coordinates: Attach a reference frame to a rigid body. and are properties of the body! 2007 M.S. Allen 3 Motion of Points on a Rigid Body Relative velocity and acceleration terms are zero because is constant! 2007 M.S. Allen 4 2 3D Rigid Body Motion 2007 M.S. Allen 5 2D Rigid Body Motion 2007 M.S. Allen 6 3 2007 M.S. Allen 7 Chasles Theorem = + 2007 M.S. Allen 8 4 Crank Example: 1.17 in Notes Find velocity and acceleration of point P for the given geometry and motion of arm AB. 2007 M.S. Allen 9 3D Interconnections 2007 M.S. Allen 10 5 Example 3D Mechanism 2007 M.S. Allen 11 6 ...

Michigan State University, ME 221

Excerpt: ... ME 221 Statics Lecture #21 Sections 5.1 5.4 ME 221 Lecture 21 1 Homework #8 Chapter 9 problems: 42, 43, 50 & 55 Chapter 5 problems: 11, 13, 16, 20, 24 & 25 See Angel for additional information Due Friday, October 24 ME 221 Lecture 21 2 Quiz #5 Friday, October 24 ME 221 Lecture 21 3 Note: No office hours on Tuesday, October 21 ME 221 Lecture 21 4 Chapter 5 Equilibrium of Rigid Bodies ME 221 Lecture 21 5 Equilibrium of Rigid Bodies Equilibrium equations Free body diagrams Modeling supports Example ME 221 Lecture 21 6 Equilibrium of Rigid Bodies Newton's Second law states that if there is a net force acting on a body, then this will cause motion of the rigid body. If there is no motion, then the object is said to be in equilibrium. ME 221 Lecture 21 7 Equilibrium Equations When the force system is replaced by a resultant force and moment that are zero, the rigid body is in equ ...

UF, CGS 3220

Excerpt: ... CGS 3220 Lecture 10 Dynamic Rigid Bodies Introduction to Computer Aided Modeling Instructor: Brent Rossen Overview Creating a Passive Rigid Body Creating an Active Rigid Body Adding a gravity field Simulating dynamics Setting rigid body attributes Setting rigid body keyframes Caching a dynamic simulation Rigid Bodies In animation, there are often scenes that are better done through simulation. Collisions between objects, for example, are often too complex to animate by hand. In that case, we set up the forces to govern the scene and use dynamic simulation. Active and Passive Active Rigid Bodies react to dynamics fields, collisions and springs, but not to keys Passive Rigid Bodies can have active bodies collide with them. You can key their attributes, but dynamics has no effect on them. Let's try out some dynamics with a test scene, File > New Test Scene Create a polygonal cube and scale it to make the floor, rename it floor Create a sphere and a cube and place them side by side above the floor Ac ...

Cornell, WB 1310

Excerpt: ... Multibody Dynamics A wb1310 Arend L. Schwab Laboratory for Engineering Mechanics Delft University of Technology Spring 2009 2nd lecture Contents Lecture 1th 2nd Topic Introduction, Teamup. Newton-Euler eqns of motion for a 3D rigid body. Modelling o ...

Vanderbilt, PHYSICS 116

Excerpt: ... nt. The acceleration of the center-of-mass for N particles Having obtained an expression for the velocity of the center-of-mass we can now look at the acceleration of the center-of-mass aCM = dvCM 1 = dt M N mi i=1 dvi 1 = dt M N mi a i i=1 Again doing the multiplication by M we get the Newton's Second Law expression N N M aCM = i=1 mi a i = i=1 Fi = Fext The fictitious total mass M is moving with an acceleration aCM as given by a total external force. If the total external force is zero (only internal forces are acting) then the acceleration of the center-of-mass point is zero. This also means that the total momentum of the system, ptot is constant. Lecture 12: Rotational Kinematics and Dynamics 3 CHAPTER 9: Rotation of a Rigid Body about a Fixed Axis Up until know we have always been looking at "point particles" or the motion of the centerofmass of extended objects. In this chapter we begin the study of rotations of an extended object about a fixed axis. Such objects are called rigid bodies b ...

UCSD, MAE 130

Excerpt: ... D.2 MAE 130B: Mechanics II: Dynamics MAE 130B Mechanics II: Dynamics Catalog Data: MAE 130B Mechanics II: Dynamics (4) (Cross-listed with SE101B) Kinematics and kinetics of particles in 2-D and 3-D motion by using vector representation. Orbital mechanics. Work, energy, and power. Conservative forces, conservation principles. Momentum, impulse motion, and impact. Rigid body kinetics and kinematics, energy and momentum; Coriolis acceleration, Euler angles. Prerequisites: Math. 21D and MAE 130A or SE 101A with grades of C- or better. Textbook, Required Materials: Beer and Johnston, Vector Mechanics for Engineers, Sixth Edition, McGraw Hill, 1996. Prerequisites by topic: Integral and differential calculus, differential equations, engineering statics. Class/Laboratory Schedule: 4 lecture hours per week Course Topics: 1. Kinematics and kinetics of particles, energy and momentum methods, central impacts 2. System of particles 3. Kinematics of rigid bodies , Coriolis acceleration 4. Kinematics and kinetics of plane mo ...

Berkeley, PHYSICS 9697

Excerpt: ... Physics 221A Fall 1996 Homework 9 Due Saturday, November 2, 1996 Reading Assignment: Sakurai pp. 195-206, Notes 12, Notes 13. I am also handing out Notes 14, if you want to read ahead on next week's lectures. 1. Show that if any operator commutes wi ...

University of Illinois, Urbana Champaign, CS 598

Excerpt: ... 1. Good afternoon, everyone. Today I'm going to give a presentation on Timewarp Rigid Body Simulation, a SIGGRAPH 2000 paper. The author is a researcher in Mitsubishi Electric Research Lab. 2. Rigid body simulation has become a mature technology recently. Major issues have been well studied and made practical. But there's still room for significant improvement. The motivation of this paper is to simulate a vast number of moving and interacting objects, and what it concerns with is general rigid body simulation, indicating that the rigid bodies have nontrivial geometries. The key idea is that although rigid body dynamics is a continuous process, it exhibits many features of a discrete one, so we can avoid the time-consuming synchronization as far as possible. 3. Numerous techniques have been developed to simulate large numbers of rigid bodies . Some of them focus on rigid bodies with special shapes, like spheres or polyhedra; others make some approximation without full collision detection. However, when the sys ...

Rowan, BIOMECH 08

Excerpt: ... ve Associative You should be able to add vector components, compute vector dot products and compute vector cross products. Dot product Vector product Kinematics is the study of the motion of particles and rigid bodies , disregarding forces associated with these motions. Thus, this does not involve physical laws such as Newtons laws. COORDINATE SYSTEMS Cartesian coordinates The orthogonal unit vectors are In component form Position of point P is Differentiate once with respect to time x If the coordinate system is NOT moving (fixed), then Differentiate again with respect to time y z Cylindrical coordinates For symmetry about a line The orthogonal unit vectors are Position is expressed as Note here that ez remains parallel to the z-axis, while change with rotation about the z-axis. Thus the rotation rate of the unit vectors is and the derivatives of the unit vectors are z y x Differentiating position gives Differentiating velocity gives z Spherical coordinates For symmetry about a point The ortho ...

CSU Channel Islands, ME 80

Excerpt: ... Lecture 3-9-09 Chapter 17 continued Problem 17.26 Work/power by torques: 17.41 Impulse momentum principle for a rigid body Sample 17.8 Lecture 3-11-09 Collision for rigid bodies pool balls colliding (17.118) Example 17.10 of the text 17.103 3/13/09 Problem 17.99 Problem 17.109 Problem 17.116 Problem 17.132 ...

Air Force Academy, ME 316

Excerpt: ... ME 316 2008/2009 year Lecture note 1 Lecture Note (1) Kinematics of a rigid body Table of contents: 1. Basic concepts 2. Classification of problems 3. The scope of problem solving using the equation in the GE226 course 1. Basic concepts We begin ...

Toledo, PHY 131

Excerpt: ... PHY131H1S - Jason Harlow Class 19 Hand-written notes, Monday March 16, 2009 Ch. 12, sections 12.5 to 12.11: Torque, Rotational Dynamics, Static Equilibrium, Rolling without slipping, Rigid Body motion ...