To generate constant arc points on Archimedean Spiral

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KUNDAN PRASAD
KUNDAN PRASAD 2023-12-11
评论： Mathieu NOE 2023-12-12
Dear Sir/ Mam,
The code for constant angle has been attahced. In this code i want to modify and need to generate constant arc points on Archimedean Spiral instead of constant angle
clear all
clc
% Parameters
R = 0; %outer radius
b = 2; %incerement per rev, equivalent to feed
a = -20; %inner radius
n = round((R - a)./(b)); %number of revolutions and number of
th = 2*n*pi; %angle obtained for n number of revolution, for one revoultion 2*pi
desiredAngle = 10;% Desired constant angle between points
npt= 360/desiredAngle; %% number of points in each spiral
t= ((-a/(2))*npt);
theta = 0:th/t:th;
r= ((a + b.*theta./(2*pi)));
% Interpolate points along the Archimedean spiral with constant angle
interpPoints = interp1(theta, [r', theta'], 0:th/t:th);
% Extract interpolated r and theta values
interp_r = interpPoints(:, 1);
interp_theta = interpPoints(:, 2);
% Convert polar coordinates to Cartesian coordinates
x =(-interp_r.* cos(interp_theta))';
y = (-interp_r.* sin(interp_theta))';
% Plot the Archimedean spiral and equidistant points in terms of angle
figure;
plot((-r.* cos(theta)), (-r .* sin(theta)), 'LineWidth', 2); % Original Archimedean Spiral
hold on;
plot(x, y, '-o'); % Equidistant Points in terms of Angle
axis equal;
xlabel('X-axis');
ylabel('Y-axis');
title('Spiral Toolpath with Constant Angle');
legend('Original Archimedean Spiral', 'Equidistant Points in terms of Angle');

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Mathieu NOE
Mathieu NOE 2023-12-11
Ran in:
hello
try this
also I prefer to have
R = 20; %outer radius
a = 0; %inner radius
instead of
R = 0; %outer radius
a = -20; %inner radius
as for me inner radius (or start point) is at the center and not the most outer point - same comment for the other point
code
% Parameters
R = 20; %outer radius
b = 2; %incerement per rev, equivalent to feed
a = 0; %inner radius
n = round((R - a)./(b)); %number of revolutions and number of
th = 2*n*pi; %angle obtained for n number of revolution, for one revoultion 2*pi
theta = linspace(0,th,n*360);
r= a + b.*theta./(2*pi);
% Convert polar coordinates to Cartesian coordinates
xr = r.* cos(theta);
yr = r.* sin(theta);
%% constant arc code
% curvilinear abscissa : s = integral of a*sqrt(1+theta²)
y = b*sqrt(1+theta.^2);
s = cumtrapz(theta,y);
desiredArcsPoints = 3*360; % n*360;% Desired arcs points
sd = linspace(0,s(end),desiredArcsPoints);
% Interpolate points along the Archimedean spiral with constant arc
ti = interp1(s, theta, sd); % angle values with constant arc spacing
r= a + b.*ti./(2*pi);
% Convert polar coordinates to Cartesian coordinates
x = r.* cos(ti);
y = r.* sin(ti);
% Plot the Archimedean spiral and equidistant points in terms of angle
figure;
plot(xr, yr, 'LineWidth', 2); % Original Archimedean Spiral
hold on;
plot(x, y, '-o'); % Equidistant Points in terms of Angle
axis equal;
xlabel('X-axis');
ylabel('Y-axis');
title('Spiral Toolpath with Constant Arc');
legend('Original Archimedean Spiral', 'Equidistant Points in terms of Arc');
  2 个评论
KUNDAN PRASAD
KUNDAN PRASAD 2023-12-11
移动：Mathieu NOE 2023-12-12
Thank you for informative details provide on the code.
Still i have one question?
How we can make the constant angle in the inner portion of the spiral toolpath with constant arc.
i.e., if total diameter is 40; then 10 mm is made with constant angle and rest is 30 mm diameter with constant arc.
Looking for the reply of question.
Once again thank you
Mathieu NOE
Mathieu NOE 2023-12-12
Ran in:
try this
clear all
clc
% Parameters
R2 = 40; %outer radius (between this radius and R1 is constant arc increment)
R1 = 10; %intermediate radius (below this radius is constant angle increment)
b = 2; %incerement per rev, equivalent to feed
a = 0; %inner radius
n = round((R2 - a)./(b)); %number of revolutions and number of
th = 2*n*pi; %angle obtained for n number of revolution, for one revoultion 2*pi
theta = linspace(0,th,n*360);
r= a + b.*theta./(2*pi);
% Convert polar coordinates to Cartesian coordinates
xr = r.* cos(theta);
yr = r.* sin(theta);
%% constant angular increment section
ind1 = (r<=R1);
x1 = xr(ind1);
y1 = yr(ind1);
%% constant arc increment section
ind2 = (r>R1);
theta2 = theta(ind2);
% curvilinear abscissa : s = integral of a*sqrt(1+theta²)
y = b*sqrt(1+theta2.^2);
s = cumtrapz(theta2,y);
desiredArcsPoints = 3*360; % n*360;% Desired arcs points
sd = linspace(0,s(end),desiredArcsPoints);
% Interpolate points along the Archimedean spiral with constant arc
ti = interp1(s, theta2, sd); % angle values with constant arc spacing
r= a + b.*ti./(2*pi);
% Convert polar coordinates to Cartesian coordinates
x = r.* cos(ti);
y = r.* sin(ti);
% combine both data sets (below and above R1)
x = [x1 x];
y = [y1 y];
% Plot the Archimedean spiral
figure;
plot(xr, yr, 'LineWidth', 2); % Original Archimedean Spiral
hold on;
plot(x, y, '-o'); % Equidistant Points in terms of Angle then Arc
axis equal;
xlabel('X-axis');
ylabel('Y-axis');
title('Spiral Toolpath with Constant Arc');
legend('Original Archimedean Spiral', 'Equidistant Points in terms of Angle / Arc');

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