16. Toy Car Downhill
Animations
Input File
# rolling_car_2d.mbd
#-----------------------------------------------------------------------------
# [Data Block]
begin: data;
problem: initial value;
end: data;
#-----------------------------------------------------------------------------
# [ Block]
begin: initial value;
initial time: 0.;
final time: 2.;
time step: 1.e-4;
max iterations: 10;
tolerance: 1.e-7;
end: initial value;
#-----------------------------------------------------------------------------
# [Control Data Block]
begin: control data;
skip initial joint assembly;
output frequency: 50;
structural nodes: 8;
rigid bodies: 3;
joints: 11;
forces: 2;
gravity;
end: control data;
#-----------------------------------------------------------------------------
# Design Variables
set: real L = 0.1; # [m] Wheel Base
set: real M = 0.1; # [kg] Mass
set: real D = 0.05; # [m] Chassis Height
set: real K = 100.; # [N/m] Spring Rate
set: real C = 1; # [Ns/m] Shock Absorber
set: real Kc = 5000.; # [N/m] Contact Stiffness
set: real Ec = 1.2; # [-] Contact Stiffness Exponent
set: real Cc = 0.1; # [Ns/m] Contact Damping
set: real Dc = 0.0001;# [m] Contact Damping Activation Depth
set: real Delta_Road = 0.0001; #[m]
#-----------------------------------------------------------------------------
# Intermediate Variables
set: real I = M*L^2./12.; # Moment of Inertia of Chassis
#-----------------------------------------------------------------------------
# Reference Labels
set: integer Ref_RearWheel = 1;
# Node Labels
set: integer NoSta_Ground = 1;
set: integer NoDyn_Chassis = 2;
set: integer NoDyn_FrontWheel = 3;
set: integer NoDyn_RearWheel = 4;
set: integer NoDyn_Road1 = 5;
set: integer NoDyn_Road2 = 6;
set: integer NoDum_FrontWheel = 7;
set: integer NoDum_RearWheel = 8;
# Body Labels
set: integer Body_Chassis = 1;
set: integer Body_FrontWheel = 2;
set: integer Body_RearWheel = 3;
# Joint Labels
set: integer JoClamp_Ground = 1;
set: integer JoInp_Ground_Chassis = 2;
set: integer JoRevrot_Ground_Chassis = 3;
set: integer JoInlin_Chassis_FrontWheel = 4;
set: integer JoPrism_Chassis_FrontWheel = 5;
set: integer JoDfmd_Chassis_FrontWheel = 6;
set: integer JoInlin_Chassis_RearWheel = 7;
set: integer JoPrism_Chassis_RearWheel = 8;
set: integer JoDfmd_Chassis_RearWheel = 9;
set: integer JoTotp_Road1 = 10;
set: integer JoTotp_Road2 = 11;
# Force Labels
set: integer FoStrin_Normal_FrontWheel_Road1 = 1;
set: integer FoStrin_Normal_RearWheel_Road2 = 2;
#-----------------------------------------------------------------------------
# Scalar Functions
include: "sf_cubstep.sub";
include: "sf_Fun_Road.sub";
#-----------------------------------------------------------------------------
# Intermediate Variables
set: real Road1_Height_Ini = model::sf::Fun_Road(L);
set: real Road2_Height_Ini = model::sf::Fun_Road(0.);
set: real Road1_Angle_Ini = atan((model::sf::Fun_Road(L+Delta_Road)-model::sf::Fun_Road(L))/Delta_Road);
set: real Road2_Angle_Ini = atan((model::sf::Fun_Road(Delta_Road)-model::sf::Fun_Road(0.))/Delta_Road);
#-----------------------------------------------------------------------------
# References
reference: Ref_RearWheel,
0., 0., Road2_Height_Ini, # absolute position
eye, # absolute orientation
null, # absolute velocity
null; # absolute angular velocity
#-----------------------------------------------------------------------------
# [Nodes Block]
begin: nodes;
#-----------------------------------------------------------------------------
# Nodes
structural: NoSta_Ground, static,
null, # absolute position
eye, # absolute orientation
null, # absolute velocity
null; # absolute angular velocity
structural: NoDyn_Chassis, dynamic,
reference, Ref_RearWheel, L/2., 0., D, # absolute position
reference, Ref_RearWheel, euler, pi/2., 0., 0., # absolute orientation
reference, Ref_RearWheel, null, # absolute velocity
reference, Ref_RearWheel, null; # absolute angular velocity
structural: NoDyn_FrontWheel, dynamic,
reference, Ref_RearWheel, L, 0., 0., # absolute position
reference, Ref_RearWheel, eye, # absolute orientation
reference, Ref_RearWheel, null, # absolute velocity
reference, Ref_RearWheel, null; # absolute angular velocity
structural: NoDyn_RearWheel, dynamic,
reference, Ref_RearWheel, null, # absolute position
reference, Ref_RearWheel, eye, # absolute orientation
reference, Ref_RearWheel, null, # absolute velocity
reference, Ref_RearWheel, null; # absolute angular velocity
structural: NoDyn_Road1, dynamic,
L, 0., Road1_Height_Ini, # absolute position
euler, 0., -Road1_Angle_Ini, 0., # absolute orientation
null, # absolute velocity
null; # absolute angular velocity
structural: NoDyn_Road2, dynamic,
0., 0., Road2_Height_Ini, # absolute position
euler, 0., -Road2_Angle_Ini, 0., # absolute orientation
null, # absolute velocity
null; # absolute angular velocity
structural: NoDum_FrontWheel, dummy, NoDyn_FrontWheel,
relative frame, NoDyn_Road1;
structural: NoDum_RearWheel, dummy, NoDyn_RearWheel,
relative frame, NoDyn_Road2;
end: nodes;
#-----------------------------------------------------------------------------
# Plugin Variables
set: [node, DX1, NoDyn_FrontWheel, structural, string="X[1]"];
set: [node, DX2, NoDyn_RearWheel, structural, string="X[1]"];
set: [node, DZ1_Dum, NoDum_FrontWheel, structural, string="X[3]"];
set: [node, DZ2_Dum, NoDum_RearWheel, structural, string="X[3]"];
set: [node, VZ1_Dum, NoDum_FrontWheel, structural, string="XP[3]"];
set: [node, VZ2_Dum, NoDum_RearWheel, structural, string="XP[3]"];
#-----------------------------------------------------------------------------
# [Elements Block]
begin: elements;
#-----------------------------------------------------------------------------
# Bodies
body: Body_Chassis, NoDyn_Chassis,
M, # mass
null, # relative center of mass
diag, 1., 1., I; # inertia matrix
body: Body_FrontWheel, NoDyn_FrontWheel,
1.e-6, # mass
null, # relative center of mass
diag, 1.e-9, 1.e-9, 1.e-9; # inertia matrix
body: Body_RearWheel, NoDyn_RearWheel,
1.e-6, # mass
null, # relative center of mass
diag, 1.e-9, 1.e-9, 1.e-9; # inertia matrix
#-----------------------------------------------------------------------------
# Joints
joint: JoClamp_Ground,
clamp,
NoSta_Ground,
position, node,
orientation, node;
joint: JoInp_Ground_Chassis,
in plane,
NoSta_Ground,
null, # relative plane position
0., 1., 0., # relative normal direction
NoDyn_Chassis;
joint: JoRevrot_Ground_Chassis,
revolute rotation,
NoSta_Ground,
hinge,
euler, pi/2., 0, 0., # relative orientation matrix
NoDyn_Chassis;
joint: JoInlin_Chassis_FrontWheel,
in line,
NoDyn_Chassis,
reference, Ref_RearWheel, L, 0., D, # relative line position
reference, Ref_RearWheel, eye, # relative line orientation
NoDyn_FrontWheel;
joint: JoPrism_Chassis_FrontWheel,
prismatic,
NoDyn_Chassis,
hinge, reference, global, eye, # relative orientation matrix
NoDyn_FrontWheel;
joint: JoDfmd_Chassis_FrontWheel,
deformable displacement joint,
NoDyn_Chassis,
reference, Ref_RearWheel, L, 0., D, # relative offset
hinge, reference, Ref_RearWheel, eye, # relative orientation matrix
NoDyn_FrontWheel,
null, # relative offset
linear viscoelastic isotropic,
K, # stiffness
C, # viscosity coefficient
prestrain, single, 0., 0., -1, const, D;
joint: JoInlin_Chassis_RearWheel,
in line,
NoDyn_Chassis,
reference, Ref_RearWheel, 0., 0., D, # relative line position
reference, Ref_RearWheel, eye, # relative line orientation
NoDyn_RearWheel;
joint: JoPrism_Chassis_RearWheel,
prismatic,
NoDyn_Chassis,
hinge, reference, global, eye, # relative orientation matrix
NoDyn_RearWheel;
joint: JoDfmd_Chassis_RearWheel,
deformable displacement joint,
NoDyn_Chassis,
reference, Ref_RearWheel, 0., 0., D, # relative offset
hinge, reference, Ref_RearWheel, eye, # relative orientation matrix
NoDyn_RearWheel,
null, # relative offset
linear viscoelastic isotropic,
K, # stiffness
C, # viscosity coefficient
prestrain, single, 0., 0., -1, const, D;
joint: JoTotp_Road1,
total pin joint,
NoDyn_Road1,
position, null, # relative offset
position, null, # absolute position
position constraint,
active, active, active,
component,
string, "DX1",
null,
string, "model::sf::Fun_Road(DX1)",
orientation constraint,
active, active, active,
single, 0., 1., 0,
string, "-atan((model::sf::Fun_Road(DX1+Delta_Road)\
-model::sf::Fun_Road(DX1))/Delta_Road)";
joint: JoTotp_Road2,
total pin joint,
NoDyn_Road2,
position, null, # relative offset
position, null, # absolute position
position constraint,
active, active, active,
component,
string, "DX2",
const, 0.,
string, "model::sf::Fun_Road(DX2)",
orientation constraint,
active, active, active,
single, 0., 1., 0,
string, "-atan((model::sf::Fun_Road(DX2+Delta_Road)\
-model::sf::Fun_Road(DX2))/Delta_Road)";
#-----------------------------------------------------------------------------
# Forces
force: FoStrin_Normal_FrontWheel_Road1,
follower internal,
NoDyn_Road1,
position, null, # relative arm
NoDyn_FrontWheel,
position, null, # relative arm
single, 0., 0., -1.,
string, "max(0,Kc*sign(0-DZ1_Dum)*abs(0-DZ1_Dum)^Ec\
-Cc*VZ1_Dum*model::sf::cubstep((0-DZ1_Dum)/Dc))"; # force value
force: FoStrin_Normal_RearWheel_Road2,
follower internal,
NoDyn_Road2,
position, null, # relative arm
NoDyn_RearWheel,
position, null, # relative arm
single, 0., 0., -1.,
string, "max(0,Kc*sign(0-DZ2_Dum)*abs(0-DZ2_Dum)^Ec\
-Cc*VZ2_Dum*model::sf::cubstep((0-DZ2_Dum)/Dc))"; # force value
#-----------------------------------------------------------------------------
# Gravity
gravity: 0., 0., -1., const, 9.81;
end: elements;
Subfiles
# sf_cubstep.sub
scalar function: "cubstep",
cubicspline, do not extrapolate,
-0.03, 0.00,
-0.02, 0.00,
-0.01, 0.00,
0.00, 0.00,
1.00, 1.00,
1.01, 1.00,
1.02, 1.00,
1.03, 1.00;
# sf_Fun_Road.sub
scalar function: "Fun_Road",
cubicspline, do not extrapolate,
0.000000, 0.050000,
0.010000, 0.049726,
0.020000, 0.048907,
0.030000, 0.047553,
0.040000, 0.045677,
0.050000, 0.043301,
0.060000, 0.040451,
0.070000, 0.037157,
0.080000, 0.033457,
0.090000, 0.029389,
0.100000, 0.025000,
0.110000, 0.020337,
0.120000, 0.015451,
0.130000, 0.010396,
0.140000, 0.005226,
0.150000, -0.000000,
0.160000, -0.005226,
0.170000, -0.010396,
0.180000, -0.015451,
0.190000, -0.020337,
0.200000, -0.025000,
0.210000, -0.029389,
0.220000, -0.033457,
0.230000, -0.037157,
0.240000, -0.040451,
0.250000, -0.043301,
0.260000, -0.045677,
0.270000, -0.047553,
0.280000, -0.048907,
0.290000, -0.049726,
0.300000, -0.050000,
0.310000, -0.050274,
0.320000, -0.051093,
0.330000, -0.052447,
0.340000, -0.054323,
0.350000, -0.056699,
0.360000, -0.059549,
0.370000, -0.062843,
0.380000, -0.066543,
0.390000, -0.070611,
0.400000, -0.075000,
0.410000, -0.079663,
0.420000, -0.084549,
0.430000, -0.089604,
0.440000, -0.094774,
0.450000, -0.100000,
0.460000, -0.105226,
0.470000, -0.110396,
0.480000, -0.115451,
0.490000, -0.120337,
0.500000, -0.125000,
0.510000, -0.129389,
0.520000, -0.133457,
0.530000, -0.137157,
0.540000, -0.140451,
0.550000, -0.143301,
0.560000, -0.145677,
0.570000, -0.147553,
0.580000, -0.148907,
0.590000, -0.149726,
0.600000, -0.150000,
0.610000, -0.149726,
0.620000, -0.148907,
0.630000, -0.147553,
0.640000, -0.145677,
0.650000, -0.143301,
0.660000, -0.140451,
0.670000, -0.137157,
0.680000, -0.133457,
0.690000, -0.129389,
0.700000, -0.125000,
0.710000, -0.120337,
0.720000, -0.115451,
0.730000, -0.110396,
0.740000, -0.105226,
0.750000, -0.100000,
0.760000, -0.094774,
0.770000, -0.089604,
0.780000, -0.084549,
0.790000, -0.079663,
0.800000, -0.075000,
0.810000, -0.070611,
0.820000, -0.066543,
0.830000, -0.062843,
0.840000, -0.059549,
0.850000, -0.056699,
0.860000, -0.054323,
0.870000, -0.052447,
0.880000, -0.051093,
0.890000, -0.050274,
0.900000, -0.050000,
0.910000, -0.050274,
0.920000, -0.051093,
0.930000, -0.052447,
0.940000, -0.054323,
0.950000, -0.056699,
0.960000, -0.059549,
0.970000, -0.062843,
0.980000, -0.066543,
0.990000, -0.070611,
1.000000, -0.075000,
1.010000, -0.079663,
1.020000, -0.084549,
1.030000, -0.089604,
1.040000, -0.094774,
1.050000, -0.100000,
1.060000, -0.105226,
1.070000, -0.110396,
1.080000, -0.115451,
1.090000, -0.120337,
1.100000, -0.125000,
1.110000, -0.129389,
1.120000, -0.133457,
1.130000, -0.137157,
1.140000, -0.140451,
1.150000, -0.143301,
1.160000, -0.145677,
1.170000, -0.147553,
1.180000, -0.148907,
1.190000, -0.149726,
1.200000, -0.150000,
1.210000, -0.149726,
1.220000, -0.148907,
1.230000, -0.147553,
1.240000, -0.145677,
1.250000, -0.143301,
1.260000, -0.140451,
1.270000, -0.137157,
1.280000, -0.133457,
1.290000, -0.129389,
1.300000, -0.125000,
1.310000, -0.120337,
1.320000, -0.115451,
1.330000, -0.110396,
1.340000, -0.105226,
1.350000, -0.100000,
1.360000, -0.094774,
1.370000, -0.089604,
1.380000, -0.084549,
1.390000, -0.079663,
1.400000, -0.075000,
1.410000, -0.070611,
1.420000, -0.066543,
1.430000, -0.062843,
1.440000, -0.059549,
1.450000, -0.056699,
1.460000, -0.054323,
1.470000, -0.052447,
1.480000, -0.051093,
1.490000, -0.050274,
1.500000, -0.050000;
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