Appendix
Appendix 1A
Ballistic walk model
DATA
Definition of useful values of the system UNITES : kilogram, metre and second
Definition of the system's element
elem is the matrix to define the elements of the rigid body The first column : definition of element's type
R : free rigid body (3 or 1 node)
F : CR (3 or 2 nodes) fixed to another one (sharing a node with another rigid body)
S : spring D : damper
T : rotation spring
O : special unit by Otto-Bock H : hinge
The second column : element's material, correspondence with "mat" ATTENTION : correspond to have a friction table (char) for H
The third column : the length of the element (the empty length of damper nd spring, D and S) correspondence with "lon"
The quarter column : number of the node of gravity centre of the element (valid for element R with 1 node)
F with two node : the farther node from the contact
The fifth column : About R : 1st extremity of the element, nearest to the origin % example 4 5 6 given % _______________ % 5 \ % \ * : CG % * 4 % \ % \ 6 %
% About F (2 or 3 nodes) : the node in contact with the rigid body % example 4 5 0 or 4 5 6 given ____________________ % | | % | | % 5 \ 5 \ ----> : angle of atta % \ \ % -->\ 4 4 * % \ % ---->\ 6
The sixth column: the last node, this compartment must be empty for the element R that has one node and for the element F that has two nodes
The seventh column: referring to table angle the table atta (in degree) is useful only for the element F. It allows to define the angle that it forms with another rigid body.
ATTENTION: for one chain of the body F, must add that angle !! We have 4 rigid bodies, 3 masses, 3 hinges = 10
elem = ['R' 1 0 1 0 0 0 ; % 1 'R' 2 2 2 1 3 0 ; % 2 'H' 1 0 0 3 4 0 ; % 3 'R' 3 3 5 4 6 0 ; % 4 'R' 4 0 6 0 0 0 ; % 5 'R' 3 3 8 7 9 0 ; % 6 'H' 1 0 0 6 7 0 ; % 7 'H' 1 0 0 9 10 0 ; % 8 'R' 2 2 11 10 12 0; % 9 'R' 1 0 12 0 0 0 ]; % 10 atta = [] ;
Definition of the system's parameter
definition of gravity vector g = 9.81 ;
pente = (5) ;
%pente = (0.004/pi*180) ;
length of the element and position of CG (in m)
length of 4 different elements ( foots, calf muscle, leg, trunk) l1 = 0 ; cg1_h = 0 ; l2 = 0.3 ; cg2_h = 0.5*0.3 ; l3 = 0.401 ; cg3_h = 0.5*0.401 ; l4 = 0 ; cg4_h = 0 ; cg1_b = l1-cg1_h ; cg2_b = l2-cg2_h ; cg3_b = l3-cg3_h ; cg4_b = l4-cg4_h ;
definition of the length matrix
lon = [ l1 cg1_h cg1_b ; l2 cg2_h cg2_b ; l3 cg3_h cg3_b ; l4 cg4_h cg4_b] ;
definition of the mass properties (in kg) m1 = 1 ; m2 = 4 ; m3 = 8 ; m4 = 40 ;
J1 = 0 ; J2 = m2*l2^2/12 ; J3 = m3*l2^2/12 ; J4 = 0 ;
Matrix of material properties of the elements Correspondence with d (kg/(m.s)) and s (kg/m) : d : Pour Otto : 2*3 values of compression/extension amor = a*(1/x^2) + b*(1/x) + c Standard : the third term
s : just the value of the stiffness (130.1e3 N/m for elasto Otto 8.75.1e3 N/m for noir Otto)
For Otto : -> Damper yellow comp : -2.8189*1e-4*(1/v^2) + 3.0939*(1/v) + 355.1361 -> Damper yellow exte : -0.0051*(1/v^2) + 24.1402*(1/v) + 5.6059*1e4 or
-> Damper yellow comp : 2.1443*(1/v) + 885.0653 -> Damper yellow exte : 7.0819*(1/v) + 6.5579*1e4 and
-> Spring black comp : 213.5932*(1/v) - 4.9275*1e3 -> Spring black exte : 146.3288*(1/v) - 8.8085*1e3
-> Damper yellow comp : exp(2.3881*1e5*v^2 -1.4109*1e3*v + 9.2596) -> Damper yellow exte : exp(1.7019*1e4*v^2 - 166.1487*v + 11.3879) and
-> Spring black comp : exp(2.7695*1e5*v^2 - 1.7719*1e3*v + 13.8115) -> Spring black exte : exp(2.7195*1e5*v^2 - 1.8049*1e3*v + 13.4337)
mat = [ m1 J1 0 0 ; m2 J2 0 0 ; m3 J3 0 0 ; m4 J4 0 0 ] ; d = [ 213.5932 , -4.9275*1e3 , 146.3288 , -8.8085*1e3 ] ; s = [ 18.75*1e3 , 0 ; 130*1e3 , 1 ] ;
Hinge’s friction coefficient
char = [ 0 ];
Definition of the system's environment
Fixing vector of one node 1st column = node in question
the three following correspond to have these ddls blocked (x, y, t) if the value is 1 : the ddl is blocked
if the value is 0 : the ddl is free
the three last correspond to the initial condition (value) exp : x(6)=2 and y(6)=0, and t free : fix = [6 1 2 0 2 0 0]
fix = [] ;
Fixing vector of the node which is know the parameters 1st column = node in question
the three following correspond to have those ddls blocked (x, y, t) if the value is 1 : the ddl is blocked
if the value is 0 : the ddl is free
fix_in = [ 12 1 1 0 'a' 'b' 0 ] ;
The additional constraints could appear;
the lines represent one additional unilateral constrain, they are formed in a four values group as follow
1 : number of the concerned node
2,3,4 : coef. of the ddls in the expression of the constrain, as in the model: 2*x3-y3+t6 < 9 for 3 [2 -1 0]
5 : it corresponds to have the costant, if the example on the top is taken again,it is [-9] 6 et 7 : correspond to have penalty on Kt and Ct respectively
ATTENTION : in the case of it has here different(various) temporany constrain (x1 = 2 et x7 + x8 = 0), it is necessary to keep the same size for each line in the matrix con_temp Here the example:
% _______ : place for the fictive node % con_temp [ 1 1 0 0 0 0 0 0 -2 Kt1 Ct1 ;
% 7 1 0 0 8 1 0 0 0 Kt2 Ct2 ]
con_temp = [ 2 0 0 1 4 0 0 -1 0 1000 1000 ; 8 0 0 1 11 0 0 -1 0 1000 1000 ];
ATTENTION, h doesn't modify only Kt, Ct et f are modified The permanent additional constrain, the same of con_temp, % if there's not a penalty coefficient
con_perm = [] ;
% Modification of h and B stocking the lambda, the size of lambda is equal to get it from h
lambda_0 = zeros(32,1) ;
non-conservative force doing on the system
The first column correspond to have the symbolic expression of the reaction force. ATTENTION : to the reaction force The following on DDL (and not on a node) to which apply the force
ex1 = '-40*(1/(t+1))' ; ex2 = '-10*(1/(t+1))' ; ex3 = '-25*(1/(t+1))' ; ex4 = '1*(1/(t+1))' ; force_nc = [] ;
Definition of the initial condition of the system
stocking of the ddls of the elements
ref : it permits to define the coordinate of the first node that will be as reference for putting the other
position : it permits one by one the elements in order to place their nodes 1st line : correspond to the element's number in the element's table
2nd line : correspond to the number of the node ALREADY DEFINED from wich the node of the element in question will be put on.
expl : we have alredy defined the rigid element I with the nodes 1,2 and 3. we want now to do the same with another rigid element II with the nodes 4, 5 et 6.
It is given : % __________________ % 1 | % | % 2 * % | % 3 | 4 % \ % * 6 % \ % \ 5 %
3rd line : Just for the spring and the damper.
It lets to give out simply the two nodes ALREADY DEFINED, that are linked with the spring and the damper.
ATTENTION: if the angle value is between -90 and 90 put 0 if the angle value is between 90 et 270 put 1
4th line : The angle that the rigid body forms with vertical line (axis) nb_node = 12 ; ref = [ 1 0 0 180] ; position = [ 2 1 0 180 ; 4 3 0 180 ; 6 6 0 -17; 9 9 0 -25 ]; %ref = [ 1 0 0 180+(0.1534*180/pi)] ; %position = [ 2 1 0 180+(0.1534*180/pi) ;
4 3 0 180+(0.1534*180/pi) ; 6 6 0 -(0.1534*180/pi); 9 9 0 -(0.1534*180/pi) ];
Initial velocity
For every line : 1st term : number of the node
2nd term : the value of initial velocity for x 3rd term : the value of initial velocity for y 4er term : the value of inizial velocity for t
vit = [7 0 0 2.5 ] ; %tt1=0.1534; %ttp1=-0.1561*sqrt(g/(l2+l3)); %tt2=-tt1; %ph=+tt1-tt2; %php=cos(-ph)*(1-cos(-ph))*ttp1/cos(-ph); %ttp2=-php+ttp1; %vit = [1 , 0 , 0 , ttp1; % 2 -l2/2*ttp1*cos(tt1) , l2/2*ttp1*sin(tt1) , ttp1; % 3 -l2*ttp1*cos(tt1) , l2*ttp1*sin(tt1) , ttp1; % 4 -l2*ttp1*cos(tt1) , l2*ttp1*sin(tt1) , ttp1; % 5 -(l2+l3/2)*ttp1*cos(tt1) , (l2+l3/2)*ttp1*sin(tt1) , ttp1; % 6 -(l2+l3)*ttp1*cos(tt1) , (l2+l3)*ttp1*sin(tt1) , ttp1; % 7 -(l2+l3)*ttp1*cos(tt1) , (l2+l3)*ttp1*sin(tt1) , ttp2; % 8 -(l2+l3)*ttp1*cos(tt1)+l3/2*cos(tt2)*ttp2, (l2+l3)*ttp1*sin(tt1)-l3/2*sin(tt2)*ttp2,ttp2; % 9 -(l2+l3)*ttp1*cos(tt1)+l3*cos(tt2)*ttp2 , (l2+l3)*ttp1*sin(tt1)-l3*sin(tt2)*ttp2 , ttp2; % 10 -(l2+l3)*ttp1*cos(tt1)+l3*cos(tt2)*ttp2 , (l2+l3)*ttp1*sin(tt1)-l3*sin(tt2)*ttp2 , ttp2;
% 11 -(l2+l3)*ttp1*cos(tt1)+(l3+l2/2)*cos(tt2)*ttp2 , (l2+l3)*ttp1*sin(tt1) – (l3+l2/2)*sin(tt2)*ttp2 , ttp2;
% 12 -(l2+l3)*ttp1*cos(tt1)+(l2+l3)*cos(tt2)*ttp2 , (l2+l3)*ttp1*sin(tt1)- (l2+l3)*sin(tt2)*ttp2 , ttp2;] ;
Appendix 2A.
Model used in the experiment
DATA
Definition of useful values of the system UNITES : kilogram, metre and second
Definition of the system's element
elem is the matrix to define the elements of the rigid body The first column : definition of element's type
R : free rigid body (3 ou 1 noeud)
F : CR (3 ou 2 nodes) fixed to another one (sharing a node with another rigid body)
S : spring D : damper
T : rotation spring
O : special unit by Otto-Bock H : hinge
The second column : element's material, correspondence with "mat" ATTENTION : correspond to have a friction table (char) for H
The third column : he lenght of the element (the empty lenght of damper and spring, D and S) correspondence with "lon"
The quarter column : number of gravity centre of the element (valid for element R with 1 node)
H : 0
The fifth column : About R : 1st extremity of the element, nearest to the origin example 4 5 6 given _______________ 5 \ \ * : CG * 4 \ \ 6
About F (2 or 3 nodes) : the node in contact with the rigid body exemple 4 5 0 or 4 5 6 given ______________ | | | | 5 \ 5 \ ----> : angle of atta \ \ -->\ 4 4 * \ ---->\ 6
The sixth column : the last node, this compartment must be empty for the element R that has one node and for the element F that has two nodes
The seventh column : referring to table ang the table atta (in degree) is useful only for the element F. It allows to define the angle that it forms with another rigid body. ATTENTION : for one chain of the body F, must add that angle !!
elem = [ 'R' 3 2 2 1 3 0 ; % 1 The joint element
'F' 0 2 4 3 0 1 ; % 2 until element 26 there is the scheme of the
prostheses 'F' 0 4 5 4 0 3 ; % 3 'F' 0 5 6 4 0 4 ; % 4 'R' 6 0 6 0 0 0 ; % 5 'R' 7 7 7 8 9 0 ; % 6 'F' 0 8 10 7 0 5 ; % 7 'R' 9 0 10 0 0 0 ; % 8 'H' 1 0 0 4 8 0 ; % 9 'R' 10 10 11 12 13 0 ; % 10 'F' 0 11 14 11 0 6 ; % 11 'R' 12 0 14 0 0 0 ; % 12 'H' 1 0 0 5 12 0 ; % 13 'R' 13 13 15 16 17 0 ; % 14 'F' 0 14 18 15 0 7 ; % 15 'R' 15 0 18 0 0 0 ; % 16 'F' 0 17 19 16 0 9 ; % 17 'H' 1 0 0 16 9 0 ; % 18 'R' 18 18 20 21 22 0 ; % 19 'F' 0 19 23 22 0 10 ; % 20 'R' 20 0 23 0 0 0 ; % 21 'H' 1 0 0 13 21 0 ; % 22 'H' 1 0 0 19 22 0 ; % 23 'O' 22 22 24 25 26 0 ; % 24 'H' 1 0 0 13 25 0 ; % 25 'H' 1 0 0 17 26 0 ; % 26
'F' 23 23 27 17 28 11 ; % 27 The shin scheme
'R' 24 24 26 0 0 0 ; % 28 The joint between the knee and the shin 'R' 26 26 28 0 0 0 ; ]; % 29 The foot
atta = [ 10 ; 10 + 64 ; 10 + 58 ; 10 - 34 ; -90 ; 90 ; 90 ; 82 ; 68 ; 62 ; -18 ] ;
Definition of the system's parameter
definition of gravity vector g = 9.81 ;
pente = (0) ;
lenght of the element and position of CG (in m) different elements' length ( foot, shin, knee scheme)
l1 = 36*1e-3 ; cg1_h = 1/2*l1 ; l2 = 25*1e-3 ; cg2_h = 1/2*l2 ; l3 = 17.7*1e-3 ; cg3_h = 0 ; l4 = 26*1e-3 ; cg4_h = 0 ; l5 = 1.7*1e-3 ; cg5_h = 0 ; l6 = 0 ; cg6_h = 0 ; l7 = 95*1e-3 ; cg7_h = 1/2*l7 ; l8 = 8.2*1e-3 ; cg8_h = 0 ; l9 = 0 ; cg9_h = 0 ;
l10 = 76.95*1e-3 ; cg10_h = (5.6/11.05)*l10 ; l11 = 2.8*1e-3 ; cg11_h = 0 ; l12 = 0 ; cg12_h = 0 ; l13 = 88.5*1e-3 ; cg13_h = (6.8/10.4)*l13 ; l14 = 1.7*1e-3 ; cg14_h = 0 ; l15 = 0 ; cg15_h = 0 ; l16 = 14.9*1e-3 ; cg16_h = 0 ; l17 = 40.25*1e-3 ; cg17_h = 0 ; l18 = 7.9*1e-3 ; cg18_h = 1/2*l18 ; l19 = 3.3*1e-3 ; cg19_h = 0 ; l20 = 0 ; cg20_h = 0 ; l21 = 89.6*1e-3 ; cg21_h = (5.6/11.55)*l21 ; l22 = 89.25*1e-3 ; cg22_h = 0.5619*l22 ; l23 = 315*1e-3 ; cg23_h = 0.5*l23 ; l24 = 0 ; cg24_h = 0 ; l25 = 0 ; cg25_h = 0 ; l26 = 0 ; cg26_h = 0 ; l27 = 0 ; cg27_h = 0 ; cg1_b = l1-cg1_h ; cg2_b = l2-cg2_h ; cg3_b = l3-cg3_h ; cg4_b = l4-cg4_h ; cg5_b = l5-cg5_h ; cg6_b = l6-cg6_h ; cg7_b = l7-cg7_h ; cg8_b = l8-cg8_h ; cg9_b = l9-cg9_h ; cg10_b = l10 - cg10_h ; cg11_b = l11 - cg11_h ; cg12_b = l12 - cg12_h ; cg13_b = l13 - cg13_h ; cg14_b = l14 - cg14_h ; cg15_b = l15 - cg15_h ; cg16_b = l16 - cg16_h ; cg17_b = l17 - cg17_h ; cg18_b = l18 - cg18_h ; cg19_b = l19 - cg19_h ; cg20_b = l20 - cg20_h ; cg21_b = l21 - cg21_h ; cg22_b = l22 - cg22_h ; cg23_b = l23 - cg23_h ; cg24_b = l24 - cg24_h ; cg25_b = l25 - cg25_h ; cg26_b = l26 - cg26_h ; cg27_b = l27 - cg27_h ;
definition of the length matrix lon = [ l1 cg1_h cg1_b ; l2 cg2_h cg2_b ; l3 cg3_h cg3_b ; l4 cg4_h cg4_b ; l5 cg5_h cg5_b ; l6 cg6_h cg6_b ; l7 cg7_h cg7_b ; l8 cg8_h cg8_b ; l9 cg9_h cg9_b ; l10 cg10_h cg10_b ; l11 cg11_h cg11_b ; l12 cg12_h cg12_b ; l13 cg13_h cg13_b ; l14 cg14_h cg14_b ; l15 cg15_h cg15_b ; l16 cg16_h cg16_b ; l17 cg17_h cg17_b ; l18 cg18_h cg18_b ; l19 cg19_h cg19_b ; l20 cg20_h cg20_b ; l21 cg21_h cg21_b ; l22 cg22_h cg22_b ; l23 cg23_h cg23_b ; l24 cg24_h cg24_b ; l25 cg25_h cg25_b ; l26 cg26_h cg26_b ; l27 cg27_h cg27_b] ;
definition of the mass properties (in kg) m1 = 0.26 ; m2 = 0 ; m3 = 0.140 ; m4 = 0 ; m5 = 0 ; m6 = 196.6*1e-3 ; m7 = 0 ; m8 = 0 ; m9 = 123.8*1e-3 ; m10 = 0 ; m11 = 0 ; m12 = 58.3*1e-3 ; m13 = 0 ; m14 = 0 ; m15 = 253.3*1e-3 ; m16 = 0 ; m17 = 0 ; m18 = 0 ; m19 = 0 ; m20 = 49.5*1e-3 ; m21 = 104.7*1e-3 ;
m22 = 143.8*1e-3 ; m23 = 920*1e-3 ; m24 = 140*1e-3 ; m25 = 140*1e-3 ; m26 = 1.28 ; m27 = 7 ; J1 = m1*l1^2/12 ; J2 = 0 ; J3 = 0 ; J4 = 0 ; J5 = 0 ; J6 = (6.86*1e4)*1e-9 ; J7 = 0 ; J8 = 0 ; J9 = (1.18*1e5)*1e-9 ; J10 = 0 ; J11 = 0 ; J12 = (3.59*1e4)*1e-9 ; J13 = 0 ; J14 = 0 ; J15 = (25.96*1e4)*1e-9 ; J16 = 0 ; J17 = 0 ; J18 = 0 ; J19 = 0 ; J20 = (4130)*1e-9 ; J21 = (6.36*1e4)*1e-9 ; J22 = (4.19*1e4)*1e-9 ; J23 = (m23*l23^2)/12 ; J24 = 0 ; J25 = 0 ; J26 = 0 ; J27 = 0 ;
Matrix of material properties of the elements Correspondence with d (kg/(m.s)) and s (kg/m) :
d : Pour Otto : 2*3 values of compression/extension amor = a*(1/x^2) + b*(1/x) + c
Standard : the third term
s : just the value of the stiffness (130.1e3 N/m for elasto Otto 18.75.1e3 N/m for black Otto)
For Otto : -> Damper yellow comp : -2.8189*1e-4*(1/v^2) + 3.0939*(1/v) + 355.1361 -> Damper yellow exte : -0.0051*(1/v^2) + 24.1402*(1/v) + 5.6059*1e4 or
-> Damper yellow comp : 2.1443*(1/v) + 885.0653 -> Damper yellow exte : 7.0819*(1/v) + 6.5579*1e4 and
-> Spring black comp : 213.5932*(1/v) - 4.9275*1e3 -> Spring black exte : 146.3288*(1/v) - 8.8085*1e3
-> Damper yellow comp : exp(2.3881*1e5*v^2 -1.4109*1e3*v + 9.2596) -> Damper yellow exte : exp(1.7019*1e4*v^2 - 166.1487*v + 11.3879) and
-> Spring black comp : exp(2.7695*1e5*v^2 - 1.7719*1e3*v + 13.8115) -> Spring black exte : exp(2.7195*1e5*v^2 - 1.8049*1e3*v + 13.4337)
mat = [ m1 J1 0 0 ; m2 J2 0 0 ; m3 J3 0 0 ; m4 J4 0 0 ; m5 J5 0 0 ; m6 J6 0 0 ; m7 J7 0 0 ; m8 J8 0 0 ; m9 J9 0 0 ; m10 J10 0 0 ; m11 J11 0 0 ; m12 J12 0 0 ; m13 J13 0 0 ; m14 J14 0 0 ; m15 J15 0 0 ; m16 J16 0 0 ; m17 J17 0 0 ; m18 J18 0 0 ; m19 J19 0 0 ; m20 J20 0 0 ; m21 J21 1 1 ; m22 J22 2 2 ; m23 J23 0 0 ; m24 J24 0 0 ;
m25 J25 0 0 ; m26 J26 0 0 ; m27 J27 0 0] ; d = [ 0, 0, 0, 0; 0, 0, 0, 0]; d = [ 213.5932 , -4.9275*1e3 , 146.3288 , -8.8085*1e3 ; -2.1443 , -885.0653 , -7.0819 , -6.5579*1e4 ] ; s = [ 0 , 0 ; 130*1e3 , 1 ] ; s = [ 18.75*1e6 , 0 ; 130*1e3 , 1 ] ;
Hinge’s friction coefficient
char = [ 0.001 ] ;
Definition of the system development
Fixing vector of one node
1st column = node in question
the three following columns correspond to have these ddls blocked (x, y, t) if the value is 1 : the ddl is blocked
if the value is 0 : the ddl is free
the three last correspond to the initial condition (value) exp : x(6)=2 and y(6)=0, and t free : fix = [6 1 2 0 2 0 0]
fix = [ 1 1 1 1 0 0 0];
The additional constrains could appear;
t he lines represent one additional unilateral constrain, they are formed in a four values group as follow 1 : number of the concerned node
2,3,4 : coefficient of the ddls in the expression of the constrain, as in the model: 2*x3-y3+t6 < 9 for 3 [2 -1 0]
5 : it corresponds to have the constant, if the example on the top is taken again, it is [-9] 6 et 7 : correspond to have penalty on Kt and Ct respectively
ATTENTION : in the case of it has here different(various) temporary constrain (x1 = 2 et x7 + x8 = 0), it is necessary to keep the same size for each line in the matrix con_temp
Here the example:
place for the fictive node con_temp [ 1 1 0 0 0 0 0 0 -2 Kt1 Ct1 ; 7 1 0 0 8 1 0 0 0 Kt2 Ct2 ]
con_temp = [ 7 0 0 1 4 0 0 -1 11.82260917*pi/180 1000 1000 ] ;
ATTENTION, h doesn't modify only Kt, Ct et f are modified
The permanent additional constrain, the same of con_temp, if there's not a penalty coefficient
con_perm = [] ; % Modification of h and B
stocking the lambda, the size of lambda is equal to get it from h?
lambda_0 = zeros(82,1) ;
non-conservative force doing on the system
The first column correspond to have the symbolic expression of the reaction force. ATTENTION
to the reaction force
The following on DDL (and not on a node) to which apply the force force_nc = [] ;
Definition of the initial condition of the system
stocking of the ddls of the elements
ref : it permits to define the coordinate of the first node that will be as reference for putting the other
position : it permits one by one the elements in order to place their nodes 1st line : correspond to the element's number in the element's table
2nd line : correspond to the number of the node ALREADY DEFINE from which the node of the element in question will be put on.
expl : we have already defined the rigid element I with the nodes 1,2 and 3. we want now to do the same with another rigid element II with the nodes 4, 5 et 6.
It is given : % _______________ % 1 | % | % 2 * % | % 3 | 4 % \ % * 6 % \ % \ 5 %
3rd line : Just for the spring and the damper. It lets to give out simply the two nodes ALREADY DEFINED, that are linked with the spring and the damper.
ATTENTION, if the angle value is between -90 and 90 put 0 if the angle value is between 90 et 270 put 1
4th line : The angle that the rigid body forms with vertical line(axis)
ref = [ 1 0 0 0 ] ;
position = [ 1 1 0 0 ;To regulate 2 3 0 +10 ; 3 4 0 +10+58-1.912 ; 4 4 0 +10-34 ; 6 4 0 14.3239; To regulate 7 7 0 14.3239-90 ; 10 5 0 28.44;To regulate 11 11 0 28.44+90 ; 14 9 0 32.1544;To regulate 15 15 0 32.1544+90 ; 17 16 0 36.03+68 ; 19 13 0 15.8881; 20 22 0 28+62 ; To regulate 24 13 17 9.3048 ; 27 17 0 -18+30.09 ;]; Initial velocity For every line :
1st term : number of the node
3rd term : the value of initial velocity for y 4er term : the value of initial velocity for t
