1 Mechanical Systems Translation  Point mass concept  P  P(t) = F(t)*v(t)  Newton’s Laws & Free-body diagrams Rotation  Rigid body concept  P  P(t) = T(t)*w(t)  Newton’s laws & Free-body diagrams Transducer devices and effects

2 Mechanical translation Newton’s Laws  Every body persists in a state of uniform motion, except insofar as it may be compelled by force to change that state.  The time rate of change of momentum is equal to the force producing it.  To every action there is an equal and opposite reaction. (Principia Philosophiae, 1686, Isaac Newton)

3 Quantities and SI Units “F-L-T” system  Define F: force (Newton [N])  Define L: length (meter [m])  Define T: time (second [s])  Derive v: velocity, m: mass “M-L-T” system  Define M: mass (kilogram [kg])  Define L: length (meter [m])  Define T: time (second [s])  Derive v: velocity, F: force

4 Physical effects and engineered components Inertia effect - rigid body with mass Compliance (stiffness) effect - spring Dissipation (friction) effect - damper System boundary conditions: u motion conditions – velocity specified u force conditions - drivers and loads

5 Translational inertia Physical effect:  *dV Engineered device: rigid body “mass” Standard schematic icon (stylized picture) Standard multiport representation Standard icon equations

6 Inertia in translation: standard forms m v F1F2 1 I 1 F1 F2 F3

7 Compliance (stiffness) Physical effects:  =E*  Engineered devices: spring Standard schematic icon Standard multiport representation Standard icon equations

8 Standard translation icons 0 C

9 Dissipation (resistance) Physical effects Engineered devices: damper Standard schematic icons Standard multiport representation Standard icon equations

10 Standard translation icons 0 R

11 Free-body diagrams Purpose: Develop a systematic method for generating the equations of a mechanical system. Setup method: Separate the mechanical schematic into standard components and effects (icons); generate the equation(s) for each icon. Standard form of equations: the composite of all component equations is the initial system set; select a reduced set of key variables (generalized coordinates); reduce the initial equation set to a set in these variables.

12 Multiport modeling of mechanical translation Multiport representations of the standard icons: focus on power ports Equations for the standard icons Multiport modeling using the free-body approach

13 Multiport modeling of translation based on free-body diagrams Identify each mass point and rigid connector. Define an inertial velocity for each. Use a standard multiport component to represent each mass point Write the standard equation for each component.

14 Suitcase example Vo

15 Bobsled example See the file Bobsled report.pdf for a study of this model.