%% SI_3 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % DESCRIPTION %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %{ This script can be used to calculate angles between modular parts by measuring the cable length from part to part. Measuring is done at a distance of 'a' from the pivot point. %} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % INPUTS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % a: length in mm from pivot point to end of the rib % b: length in mm from pivot point to pivot point % c: thickness of the rib modular part % n: number of modular parts excl baseplate (1-10) % i: choose which iteration should be plotted from the experimental load % g: if g is 1 one side is plotted, g = 2 both sides are plotted % m: which modular parts should be plotted % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % OUTPUTS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Plot the eigenvalues of the system as a function of the dynamic pressure % parameter. % TBD % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % References %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Authors %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Code Creaded: 02/27/2019 % Code Author: Pieter Wiersinga % Tewente University, Enschede, The Netherlands % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % UPDATES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % {Day/Month/Year}: {Name of updater} % Enter your updates here: % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Plots setting close all; clear all; clc; set(0,'DefaultAxesFontSize',16); set(0,'DefaultTextFontSize',16); set(0,'DefaultLineLineWidth',1.5); set(0,'DefaultLineMarkerSize',5.5); set(0,'DefaultAxesFontName','Sitka Subheading')%Helvetica - default set(0,'defaultfigurecolor',[1 1 1]); %% figure(1), clf(1),hold on N = 'Dynamic matlab model deflection with increasing external force 0 - 3.0 kg'; title(N,'FontSize',10) axis equal; xlabel('X [mm]'); ylabel('Y [mm]') a = 66; %51 length in mm from pivot point to end of the rib b = 35; %30 length in mm from pivot point to pivot point c = 10; %10 thickness of the rib modular part % ------------------------- Input ----------------------------- n = 5; %number of modular parts excl baseplate (1-10) i = 7; %choose which iteration should be plotted from the experimental load g = 2; %if g is 1 one side is plotted, g = 2 both sides are plotted m = 3:n; %which modular parts should be plotted % ------------------------- Script: ----------------------------- %Measured ropelength between the ribs in mm (right), % at a distance of 'a' from the pivot point along the right side of the rib. g=g*i; %determine settings for h for loop for h= 1:g b = 35; if h <= g/2 w=1; i=h;e='-or'; else w=-1; i=h-(g/2);e='-ob'; end if i == 1 r1 = 24.8; r2 = 23.2; r3 = 25; r4 = 25; r5 = 24.5; r6 = b-c; elseif i == 2 r1 = 25; r2 = 20.8; r3 = 24; r4 = 24.1; r5 = 24.3; r6 = b-c; elseif i == 3 r1 = 25.3; r2 = 18.7; r3 = 22.6; r4 = 23; r5 = 24.6; r6 = b-c; elseif i == 4 r1 = 24.8; r2 = 16; r3 = 21.7; r4 = 23; r5 = 24.6; r6 = b-c; elseif i == 5 r1 = 24.9; r2 = 14.9; r3 = 20.3; r4 = 22.4; r5 = 23.8; r6 = b-c; elseif i == 6 r1 = 24; r2 = 13.8; r3 = 19.6; r4 = 22.7; r5 = 23.2; r6 = b-c; elseif i == 7 r1 = 24.4; r2 = 12.2; r3 = 18.6; r4 = 21.3; r5 = 23.5; r6 = b-c; else r1 = b-c; r2 = b-c; r3 = b-c; r4 = b-c; r5 = b-c; r6 = b-c; end % --------------------- Determinining angles ----------------------------- %converting measured ropelengths in vector format R = [r1,r2,r3,r4,r5,r6]; %theta initiation theta = 0; %initiation theta in radians thetadegrees = 0; %initiation theta in degrees thetavsr =0; %initiation theta vs horizontal reference in radians b= b-c; %determining angles using goniometry and abc formula for k = 1:n+1 %determination of direction of bending towards left d = 1 right d = -1 if R(k) <= b d= -1*w ; else d = 1*w ; end s1 = (2*a.^2)+ (b.^2) - R(k).^2; %calculation constant %abc formula constants sa = (4* a.^4)+ 4*(a.^2)*(b.^2); %a sb = (-4* s1 * a.^2); %b sc = (s1.^2)- 4* (a.^2) * (b.^2); %c sD = (sb.^2 - (4 * sa * sc)); %Determinant %abc formula angle calculation theta(k+1) = d * acos((-sb+sqrt(sD))./(2*sa)); %outcome of the abc solution in radians %theta2(k+1) = acos((-sb-sqrt(sD))./(2*sa)); %other (not needed) outcome of the abc solution thetadegrees(k+1) = (theta(k+1) *180 /pi); %angle variation neutral line in degrees %theta2degrees(k+1) = (theta2(k+1) *180 /pi); %angle variation neutral line in degrees end % --------------------- Neutral line definition ------------------------ x = 0; %initiation x coordinate base y = 0; %initiation y coordinate base for k = 1:n+1 x(k+1) = x(k)-d*c*sin(thetavsr(k)) - d*b*sin(thetavsr(k)); %determine next x coordinate pivotpoint y(k+1) = y(k)+c*cos(thetavsr(k)) + b*cos(thetavsr(k)); %determine next y coordinate pivotpoint thetavsr(k+1) = thetavsr(k)+ d* theta(k+1); %determine next angle neutral line vs vertical plot(x,y,e,'Linewidth',2) end %--------------------- Ribs definition and plotting --------------------- for k = 1:n+1 c1(k)= x(k)-a*cos(thetavsr(k)); %determine x coordinates rib ends left c2(k)= x(k)+a*cos(thetavsr(k)); %determine x coordinates rib ends right d1(k)= y(k)-d*a*sin(thetavsr(k)); %determine y coordinates rib ends left d2(k)= y(k)+d*a*sin(thetavsr(k)); %determine y coordinates rib ends right c3(k)= x(k)-a*cos(thetavsr(k))-d*c*sin(thetavsr(k)); %determine x coordinates rib ends left c4(k)= x(k)+a*cos(thetavsr(k))-d*c*sin(thetavsr(k)); %determine x coordinates rib ends right d3(k)= y(k)-d*a*sin(thetavsr(k))+c*cos(thetavsr(k)); %determine y coordinates rib ends left d4(k)= y(k)+d*a*sin(thetavsr(k))+c*cos(thetavsr(k)); %determine y coordinates rib ends right plot([c1(k),c2(k)],[d1(k),d2(k)],e,'Linewidth',2) %plotting ribs end thetavsrdegrees = thetavsr*180/pi; %calculation of angle vs horizontal reference in degrees Angle_degrees_to_reftotal(:,h) = thetavsrdegrees(1:n)'; %transverse vector Angle_degrees_to_prevtotal(:,h)= thetadegrees(1:n)'; %transverse vector pause (1) end hold off