Project for Modeling of Mechanical Systems - Analog IC Design | ECSE 4962, Study Guides, Projects, Research of Algorithms and Programming

Download Project for Modeling of Mechanical Systems - Analog IC Design | ECSE 4962 and more Study Guides, Projects, Research Algorithms and Programming in PDF only on Docsity! Modeling of Mechanical Systems Let’s consider a single degree-of-freedom (DOF) mechanism: motor link r2 r1 θl θm gear ratio: N = r2 / r1 Free Body Diagram motor link r2 r1 θl fc fc mg lc 1motor: m m m m m cI B r fθ θ τ+ = −!! ! 2link: sinc cI B r f mgθ θ θ+ = +" " " " "!! ! " Remove fc and use 1 2 (or )m mr r Nθ θ θ θ= =" " ! ! ! ! 2( ) ( ) sinm m m cI N I B NB N mgθ θ τ θ+ + + = +" " " " "!! ! " we obtain: θm , I Bθ θ" " " "!! ! 2 cr f sincmg θ"" , m m m mI Bθ θ!! ! mτ 1 cr f More General Multibody Systems Form the Lagrangian: L = K – P Apply the Lagrangian equation of motion: ext d L L dt τ θ θ ∂ ∂  − = ∂ ∂ ! General equation of motion: ( ) ( ) ( , ) ( )M B C Gθ θ θ θ θ θ θ τ+ + + =!! ! ! ! [ ]1 ... 0...0 i ki i i k i k ki h J J v h p ω θ ξ ξ ξ     = = =   ×    ! 1 1 2 N T T i i i i K J M Jθ θ =  =     ∑! ! For This Course The code to generate the general equation of motion is posted: pantilt.m, you just have to run it in MATLAB to obtain the expressions for M, C, G. To use pantilt.m, first put the mechanism in the zero- configuration (all angles are zero). Choose a coordinate frame. Represent pi-1,i , pi , hi in this coordinate frame. Then run pantilt.m. For simulation, you need substitute in the parameters m1, m2, I1c, I2c, p1, p2. Pan-Tilt Platform The pan-tilt platform is like a 2-link robot (O1 and O2 coincide). With motors and gears attached O2 O1 h1=[0,0,1]T h2=[0,1,0]T p12=[0,0,0]T Your Design But you haven’t chosen the motors and gears yet! So you get the parameters for the skeleton only, and you can form the composite inertia and center-of-mass location with different motors/gears combinations. Skeletal Pan mass = 0.2294 kg moment of inertia about COM (kg*m*2) Ill = 0.0007459 Tig = 0.0 T13 = 0.0 I22 = 0.0004750 123 = -0.0001031 133 = 0.0002978 P= 0,0.0125m, -0.0981m, 0.0590m]™ Skeletal Tilt ~~ De em | | | ee 0.003m, p,=[ 0, 0.003m,0]" mass = 0.07588 kg moment of inertia about COM (kg*m*2) T11 = 0.0001284 T12 = 0.0 T13 = 0.0 122 = 1.47le-6 I23 = 0.0 133 = 0.0001284 Adding Motors / Gears to Skeleton For your design, you need to • obtain m from the manufacturer’s datasheet • calculate Ic and location of CM based on some simplifying assumptions and the geometry of the part • determine p based on where you will mount the part An Example of Putting Things Together Consider the tilt axis with pulley, hub, and payload added. Putting Things Together (Cont.) 32768 Kg/m (density of Aluminum)ρ = 0.0381m (diameter of hub) 0.0630m (diameter of pulley) 0.0095m (diameter of hole) 0.0095m (thickness of hub) 0.0095m (thickness of pulley) 0.0190m (thickness of hole) hub pulley hole hub pulley hole d d d t t t d = = = = = = 1 2 3, , 0.0762m, 0.0381m, 0.0095m (dimension of payload)d d = First gather part data: Overall Dimension OVERALL DIMENSIONS FOR PANTILT S Z [1.2500 | [2.7500 | paee— 0,.0918Mm [1.2500] < =4— 0,0699M 0.0318m | ( I [3.2370] [7.9120] 0.0822m 0.2010m —— Uf link with better pictures: "BOXED DIMENSIONS AREIN INCHES SCALE 1:2 http://www.cat.rpi.edu/~potsaid/csd/lect2_modeling/lecture2_modeling.html Tonight (5pm) • Informal presentation of design project goal and problem statement (in the order of the team numbers). Bagnull, Tim 1 Helm, Chad 1 Sked, Matthew 1 Dleoge, James 1 Fronzo, Nicholas 2 Gaudet, Philip 2 Senical, Sean 2 Turnier, Justin 2 Gates, Soloman 3 Grefe, Bill 3 Heidbreder, Michael 3 Kolpak, Jeremy 3 Harris, Bill 4 Pettengill, Sabie 4 Telemaque, Enrico 4 Zweighaft, Eric 4 Damerji, Jack 5 DiLeo, Matthew 5 Ferman, Tyler Scott 5 Desi, Maureen 6 Douglass, Joel 6 Iyer, Rajiv 6 Trimarchi, Dennis 6 Addison, Jon 7 Handy, Joel 7 Schugmann, Robert 7 Next Tuesday, 1/28 (5pm) • Informal conceptual design review Next Wednesday, 1/29 (5pm) • Conceptual design memo due