How to rotate a figure around an origin that is rotating?

Hello, I'm trying to rotate a circle P(r1,theta1) around an origin given at coordinates (r,theta) that is rotating at the same time, the resulting trajectory of the point should look like the image in the right. I can make the circle P rotate around the origin (0,0) with the code below but I have no idea how to do it move as it should. As you can see in the gif it doesn't move following the red circle path, I would really appreciate any idea. Thanks!

close all, clc, clear
%% 1: Generating Data
ang = linspace(0,2*pi,50);  % Angle from 0 to 2pi
% Data to draw black fixed circle
 xp=5*cos(ang);    % Coordinate to draw black circle
 yp=5*sin(ang);    % Coordinate to draw black circle
% Data to draw outter circles pattern
ra = 1;            % Radius of inner circle
xb = ra*cos(ang);  % Coordinate to draw inner circle
yb = ra*sin(ang);  % Coordinate to draw inner circle
             
Nb=6;              % Number of balls
rho1 = 4;          % Radius of inner circle, polar coordinate

 rmb = 0.1;                           % Radius of the ball mark
 rxmb= rmb*cos(ang);                  % Coordinate to draw ball mark
 rymb= rmb*sin(ang);                  % Coordinate to draw ball mark

%% 2: Draw/Render Scenario
for angle=1:360
    %Clear the figure 
    clf
      
    % PLOT FIXED INNER CIRCLE
     plot(xp,yp, 'color', 'k');
     
     hold on
 
    % PLOT CIRCULAR PATTERN OF GRAY CIRCLES
    
                 for  iter=1:Nb          % Draw until Nb balls
                      theta1 = 2*pi*(Nb-iter)/Nb; % Angle of position inner circles, polar coordinate (same spacing)
                      [x,y] = pol2cart(theta1,rho1); % Transform polar to cartesian coordinates
                      cox=x+xb;          % Coordinate to draw moving circles
                      coy=y+yb;          % Coordinate to draw moving circles
                      balls = plot(cox,coy,'color','r'); % Plot circles
                      rotate(balls,[0 0 1],angle);   % Rotate moving pattern of circles
                 end
                 
                                      
                 % Drawing mark in the ball and rotating 
                
                 Rhom = 3;                                                                                                                            
                 Thetam = 2*pi;                                                                                                                                                                                                                 
                 [x_mb1,y_mb1] = pol2cart(Thetam,Rhom);
    
                 fill_mark_ball = fill(x_mb1 + rxmb,  y_mb1 + rymb,'r');
                 rotate(fill_mark_ball,[0 0 1],angle);
                  
    
    %% 3: Take Snapshot
    drawnow
end

[Star Strider]

See the Wikipedia article on Hypocycloid.

[MSolano]

This is exactly what I needed, I changed the equations for the hypocycloid and it worked! Thank you!!

Answer 1

[darova]

Try this

t = linspace(0,2*pi,20);
[x,y] = pol2cart(t,1);
n = 6;                     % number of small circles
h = zeros(1,n);            % pre-allocation objects
plot(5*x,5*y)
h1 = line(0,0,'marker','.');    % dot
    % draw smal circles
for i = 1:6
    h(i) = line(x+4*cosd(i/n*360),y+4*sind(i/n*360));    
end
for i = 1:20
        % rotate dot using hypocycloid formulas
    set(h1,'xdata',4*cosd(2*i)+cosd(5*i))   
    set(h1,'ydata',4*sind(2*i)-sind(5*i))
    rotate(h,[0 0 1],2,[0 0 0])     % small circles
    pause(1)
end

[MSolano]

Thank you!