用Matlab绘制推程为简谐运动,回程为等减速运动的凸轮,要求基圆半径80mm,滚子半径10mm,偏置距离10mm,形成距离30mm,角速度0.08mm,推成运动角130°,远休止角25°,回城运动角145°,进休止角60°,从动件长度30mm,要求图中标出各个从动件位置的压力角,标出最大压力角以及最小压力角的位置,从而使Matlab最终实现凸轮廓线显示变化的gif图和压力角a的变化曲线的gif图,并给出最大最小压力角值。
时间: 2023-07-15 13:13:18 浏览: 177
MATLAB在简谐运动图像教学中的应用公开课.pdf
这个问题比较复杂,需要进行凸轮设计和Matlab编程。以下是大致的步骤:
1. 根据所给的凸轮参数,计算凸轮的各个关键点坐标,例如推程、回程的起始点、终止点、顶点等等。
2. 根据滚子半径和偏置距离,计算从动件的运动轨迹,并在Matlab中绘制出来。
3. 计算从动件在每个位置的压力角,并在Matlab中标出。
4. 找出最大和最小压力角的位置,并计算其值。
5. 利用Matlab的动画功能,将凸轮轮廓线的变化和压力角的变化分别绘制成gif图。
下面是一个凸轮设计和Matlab绘图的参考代码,仅供参考:
```matlab
% 凸轮参数
Rp = 80; % 基圆半径
R = 10; % 滚子半径
e = 10; % 偏置距离
h = 30; % 形成距离
w = 0.08; % 角速度
theta1 = 130 / 180 * pi; % 推程运动角
theta2 = 25 / 180 * pi; % 远休止角
theta3 = 145 / 180 * pi; % 回程运动角
theta4 = 60 / 180 * pi; % 进休止角
% 计算各个关键点坐标
x1 = Rp * cos(theta1);
y1 = Rp * sin(theta1);
x2 = x1 + h * cos(theta1);
y2 = y1 + h * sin(theta1);
x3 = (Rp - e - R) * cos(theta2);
y3 = (Rp - e - R) * sin(theta2);
x4 = (Rp - e - R) * cos(theta4);
y4 = -(Rp - e - R) * sin(theta4);
x5 = (Rp - e - R) * cos(theta3);
y5 = -(Rp - e - R) * sin(theta3);
x6 = x5 - h * cos(theta3);
y6 = y5 - h * sin(theta3);
x7 = Rp * cos(theta2);
y7 = Rp * sin(theta2);
% 绘制凸轮轮廓线
theta = linspace(0, 2*pi, 1000);
x = Rp * cos(theta);
y = Rp * sin(theta);
for i = 1:length(theta)
if theta(i) >= 0 && theta(i) <= theta1
x(i) = (Rp + h) * cos(theta(i));
y(i) = (Rp + h) * sin(theta(i));
elseif theta(i) > theta1 && theta(i) <= pi - theta2
x(i) = x1 + h * cos(theta1) - R * cos(theta(i) - theta1 + asin((R + e)/h));
y(i) = y1 + h * sin(theta1) + R * sin(theta(i) - theta1 + asin((R + e)/h));
elseif theta(i) > pi - theta2 && theta(i) <= pi + theta2
x(i) = x3 + R * cos(theta(i) - pi + theta2 - asin((R + e)/h));
y(i) = y3 - R * sin(theta(i) - pi + theta2 - asin((R + e)/h));
elseif theta(i) > pi + theta2 && theta(i) <= 2*pi - theta3
x(i) = x4 + R * cos(theta(i) - pi - theta2 + asin((R + e)/h));
y(i) = y4 + R * sin(theta(i) - pi - theta2 + asin((R + e)/h));
elseif theta(i) > 2*pi - theta3 && theta(i) <= 2*pi - theta2
x(i) = x5 - h * cos(theta3) + R * cos(theta(i) - 2*pi + theta3 - asin((R + e)/h));
y(i) = y5 - h * sin(theta3) - R * sin(theta(i) - 2*pi + theta3 - asin((R + e)/h));
elseif theta(i) > 2*pi - theta2 && theta(i) <= 2*pi
x(i) = x6 - R * cos(theta(i) - 2*pi + theta2 - asin((R + e)/h));
y(i) = y6 + R * sin(theta(i) - 2*pi + theta2 - asin((R + e)/h));
end
end
plot(x, y);
axis equal;
% 绘制从动件运动轨迹和压力角
L = 30; % 从动件长度
x = zeros(1, 1000);
y = zeros(1, 1000);
alpha = zeros(1, 1000);
for i = 1:length(theta)
if theta(i) >= 0 && theta(i) <= theta1
x(i) = (Rp + h) * cos(theta(i));
y(i) = (Rp + h) * sin(theta(i));
alpha(i) = atan(((Rp + h) * sin(theta(i))) / L);
elseif theta(i) > theta1 && theta(i) <= pi - theta2
x(i) = x1 + h * cos(theta1) - R * cos(theta(i) - theta1 + asin((R + e)/h));
y(i) = y1 + h * sin(theta1) + R * sin(theta(i) - theta1 + asin((R + e)/h));
alpha(i) = atan((y(i) - y1 - h * sin(theta1)) / (x(i) - x1 - h * cos(theta1))) - asin((R + e) / sqrt((x(i) - x1 - h * cos(theta1))^2 + (y(i) - y1 - h * sin(theta1))^2));
elseif theta(i) > pi - theta2 && theta(i) <= pi + theta2
x(i) = x3 + R * cos(theta(i) - pi + theta2 - asin((R + e)/h));
y(i) = y3 - R * sin(theta(i) - pi + theta2 - asin((R + e)/h));
alpha(i) = atan((y(i) - y3) / (x(i) - x3)) - asin((R + e) / sqrt((x(i) - x3)^2 + (y(i) - y3)^2));
elseif theta(i) > pi + theta2 && theta(i) <= 2*pi - theta3
x(i) = x4 + R * cos(theta(i) - pi - theta2 + asin((R + e)/h));
y(i) = y4 + R * sin(theta(i) - pi - theta2 + asin((R + e)/h));
alpha(i) = atan((y(i) - y4) / (x(i) - x4)) - asin((R + e) / sqrt((x(i) - x4)^2 + (y(i) - y4)^2));
elseif theta(i) > 2*pi - theta3 && theta(i) <= 2*pi - theta2
x(i) = x5 - h * cos(theta3) + R * cos(theta(i) - 2*pi + theta3 - asin((R + e)/h));
y(i) = y5 - h * sin(theta3) - R * sin(theta(i) - 2*pi + theta3 - asin((R + e)/h));
alpha(i) = atan((y(i) - y5 - h * sin(theta3)) / (x(i) - x5 + h * cos(theta3))) - asin((R + e) / sqrt((x(i) - x5 + h * cos(theta3))^2 + (y(i) - y5 - h * sin(theta3))^2));
elseif theta(i) > 2*pi - theta2 && theta(i) <= 2*pi
x(i) = x6 - R * cos(theta(i) - 2*pi + theta2 - asin((R + e)/h));
y(i) = y6 + R * sin(theta(i) - 2*pi + theta2 - asin((R + e)/h));
alpha(i) = atan((y(i) - y6) / (x(i) - x6)) - asin((R + e) / sqrt((x(i) - x6)^2 + (y(i) - y6)^2));
end
end
hold on;
plot(x, y);
scatter(x(1), y(1), 'filled');
scatter(x(end), y(end), 'filled');
hold off;
xlabel('x');
ylabel('y');
title('Motion trajectory of follower');
axis equal;
figure;
plot(theta, alpha / pi * 180);
xlabel('theta');
ylabel('pressure angle');
title('Pressure angle of follower');
[max_alpha, max_index] = max(alpha);
[min_alpha, min_index] = min(alpha);
fprintf('Max pressure angle: %.2f at theta = %.2f\n', max_alpha / pi * 180, theta(max_index) / pi * 180);
fprintf('Min pressure angle: %.2f at theta = %.2f\n', min_alpha / pi * 180, theta(min_index) / pi * 180);
```
这段代码会绘制出凸轮的轮廓线、从动件的运动轨迹和压力角的变化曲线,以及计算出最大和最小压力角的位置和值。由于压力角的计算比较复杂,需要根据凸轮的不同部分分别进行计算,所以代码比较长。你可以根据自己的需要对其进行修改和优化。
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