2007年4月12日 星期四

機動學 作業五

5.1







5.1.1.





上臂的圖形 長度L1
arm1=[0 -L1/5;L1/5*cosd(-80) L1/5*sind(-80);L1/5*cosd(-70) L1/5*sind(-70);L1/5*cosd(-60) L1/5*sind(-60);L1/5*cosd(-50) L1/5*sind(-50);L1/5*cosd(-40) L1/5*sind(-40);L1/4*cosd(-45) L1+L1/4*sind(-45);L1/4*cosd(-30) L1+L1/4*sind(-30);L1/4*cosd(-10) L1+L1/4*sind(-10);L1/4*cosd(10) L1+L1/4*sind(10);L1/4*cosd(30) L1+L1/4*sind(30);L1/4*cosd(45) L1+L1/4*sind(45);L1/4*cosd(60) L1+L1/4*sind(60);L1/4*cosd(75) L1+L1/4*sind(75);L1/4*cosd(90) L1+L1/4*sind(90);L1/4*cosd(105) L1+L1/4*sind(105); L1/4*cosd(120) L1+L1/4*sind(120);L1/4*cosd(135) L1+L1/4*sind(135);L1/4*cosd(150) L1+L1/4*sind(150);L1/4*cosd(170) L1+L1/4*sind(170);L1/4*cosd(190) L1+L1/4*sind(190);L1/4*cosd(210) L1+L1/4*sind(210);L1/4*cosd(225) L1+L1/4*sind(225);L1/5*cosd(220) L1/5*sind(220);L1/5*cosd(230) L1/5*sind(230);L1/5*cosd(240) L1/5*sind(240) ;L1/5*cosd(250) L1/5*sind(250);L1/5*cosd(260) L1/5*sind(260);L1/5*cosd(270) L1/5*sind(270)]

下手臂的圖形 長度L2
arm2=[L2/5*cosd(80) L2/5*sind(80);L2/5*cosd(90) L2/5*sind(90);L2/5*cosd(100) L2/5*sind(100);L2/5*cosd(120) L2/5*sind(120);L2/5*cosd(140) L2/5*sind(140);L2/5*cosd(160) L2/5*sind(160);L2/5*cosd(180) L2/5*sind(180);L2/5*cosd(-160) L2/5*sind(-160);L2/5*cosd(-140) L2/5*sind(-140);L2/5*cosd(-120) L2/5*sind(-120);L2/5*cosd(-100) L2/5*sind(-100);L2/5*cosd(-90) L2/5*sind(-90);L2/5*cosd(-80) L2/5*sind(-80);L2+L2/7*cosd(-100) L2/7*sind(-100);L2+L2/7*cosd(-90) L2/7*sind(-90);L2+L2/7*cosd(-70) L2/7*sind(-70);L2+L2/7*cosd(-50) L2/7*sind(-50);L2+L2/7*cosd(-30) L2/7*sind(-30);L2+L2/7*cosd(-10) L2/7*sind(-10);L2+L2/7*cosd(10) L2/7*sind(10);L2+L2/7*cosd(30) L2/7*sind(30);L2+L2/7*cosd(50) L2/7*sind(50);L2+L2/7*cosd(70) L2/7*sind(70);L2+L2/7*cosd(90) L2/7*sind(90);L2+L2/7*cosd(100) L2/7*sind(100);L2/5*cosd(80) L2/5*sind(80)]

手掌的圖形 長度L3
palm=[L2+L3/4*cosd(-90) L3/4*sind(-90);L2+L3/4*cosd(-100) L3/4*sind(-100);L2+L3/4*cosd(-120) L3/4*sind(-120);L2+L3/4*cosd(-140) L3/4*sind(-140);L2+L3/4*cosd(-160) L3/4*sind(-160);L2+L3/4*cosd(-180) L3/4*sind(-180);L2+L3/4*cosd(-200) L3/4*sind(-220);L2+L3/4*cosd(-240) L3/4*sind(-240);L2+L3/4*cosd(-260) L3/4*sind(-260);L2+L3/4*cosd(-270) L3/4*sind(-270);L2+L3/4 L3/4;L2+L3/3+L3/3.2*cosd(30) L3/4+L3/3.2*sind(30);L2+L3/3+L3/3.2*cosd(26) L3/4+L3/3.2*sind(26);L2+L3/3+L3/8 L3/4;L2+L3/3+L3/4+L3/2*cosd(11) L3/8+L3/2*sind(11);L2+L3/3+L3/4+L3/2*cosd(9) L3/8+L3/2*sind(9);L2+L3/3+L3/4 L3/8;L2+L3/3+L3/4+L3/2*cosd(1) L3/2*sind(1);L2+L3/3+L3/4+L3/2*cosd(-1) L3/2*sind(-1);L2+L3/3+L3/4 0;L2+L3/3+L3/4+L3/2*cosd(0) -L3/8+L3/2*sind(0);L2+L3/3+L3/4+L3/2*cosd(-2) -L3/8+L3/2*sind(-2);L2+L3/3+L3/4 -L3/8;L2+L3/3+L3/4+L3/3*cosd(-2) -L3/4+L3/3*sind(-2);L2+L3/3+L3/4+L3/3*cosd(-4) -L3/4+L3/3*sind(-4);L2+L3/3+L3/4 -L3/4;L2+L3/4*cosd(-90) L3/4*sind(-90)]

line(arm1(:,1),arm1(:,2),'Color','r')
將arm1的點連起來成一圖 (紅)
line(arm2(:,1),arm2(:,2),'Color','m')
將arm2的點連起來成一圖 (粉紅)
line(palm(:,1),palm(:,2),'Color','b')
將palm的點連起來成一圖(綠)
axis equal

5.1.2.


% X1,X2,X3為輸入角度 
% L1 L2 L3分別為上手臂,下手臂及手掌的長度







function body(L1,L2,L3,X1,X2,X3) %程建立一程式函數body



theta1=-(X1-90)



theta2=-(180-X2+X1)



theta3=-(360-X3-X2+X1)



arm1=[0 -L1/5;L1/5*cosd(-80) L1/5*sind(-80);L1/5*cosd(-70) L1/5*sind(-70);L1/5*cosd(-60) L1/5*sind(-60);L1/5*cosd(-50) L1/5*sind(-50);L1/5*cosd(-40) L1/5*sind(-40);L1/4*cosd(-45) L1+L1/4*sind(-45);L1/4*cosd(-30) L1+L1/4*sind(-30);L1/4*cosd(-10) L1+L1/4*sind(-10);L1/4*cosd(10) L1+L1/4*sind(10);L1/4*cosd(30) L1+L1/4*sind(30);L1/4*cosd(45) L1+L1/4*sind(45);L1/4*cosd(60) L1+L1/4*sind(60);L1/4*cosd(75) L1+L1/4*sind(75);L1/4*cosd(90) L1+L1/4*sind(90);L1/4*cosd(105) L1+L1/4*sind(105); L1/4*cosd(120) L1+L1/4*sind(120);L1/4*cosd(135) L1+L1/4*sind(135);L1/4*cosd(150) L1+L1/4*sind(150);L1/4*cosd(170) L1+L1/4*sind(170);L1/4*cosd(190) L1+L1/4*sind(190);L1/4*cosd(210) L1+L1/4*sind(210);L1/4*cosd(225) L1+L1/4*sind(225);L1/5*cosd(220) L1/5*sind(220);L1/5*cosd(230) L1/5*sind(230);L1/5*cosd(240) L1/5*sind(240) ;L1/5*cosd(250) L1/5*sind(250);L1/5*cosd(260) L1/5*sind(260);L1/5*cosd(270) L1/5*sind(270)]



arm2=[L2/5*cosd(80) L2/5*sind(80);L2/5*cosd(90) L2/5*sind(90);L2/5*cosd(100) L2/5*sind(100);L2/5*cosd(120) L2/5*sind(120);L2/5*cosd(140) L2/5*sind(140);L2/5*cosd(160) L2/5*sind(160);L2/5*cosd(180) L2/5*sind(180);L2/5*cosd(-160) L2/5*sind(-160);L2/5*cosd(-140) L2/5*sind(-140);L2/5*cosd(-120) L2/5*sind(-120);L2/5*cosd(-100) L2/5*sind(-100);L2/5*cosd(-90) L2/5*sind(-90);L2/5*cosd(-80) L2/5*sind(-80);L2+L2/7*cosd(-100) L2/7*sind(-100);L2+L2/7*cosd(-90) L2/7*sind(-90);L2+L2/7*cosd(-70) L2/7*sind(-70);L2+L2/7*cosd(-50) L2/7*sind(-50);L2+L2/7*cosd(-30) L2/7*sind(-30);L2+L2/7*cosd(-10) L2/7*sind(-10);L2+L2/7*cosd(10) L2/7*sind(10);L2+L2/7*cosd(30) L2/7*sind(30);L2+L2/7*cosd(50) L2/7*sind(50);L2+L2/7*cosd(70) L2/7*sind(70);L2+L2/7*cosd(90) L2/7*sind(90);L2+L2/7*cosd(100) L2/7*sind(100);L2/5*cosd(80) L2/5*sind(80)]



palm=[L2+L3/4*cosd(-90) L3/4*sind(-90);L2+L3/4*cosd(-100) L3/4*sind(-100);L2+L3/4*cosd(-120) L3/4*sind(-120);L2+L3/4*cosd(-140) L3/4*sind(-140);L2+L3/4*cosd(-160) L3/4*sind(-160);L2+L3/4*cosd(-180) L3/4*sind(-180);L2+L3/4*cosd(-200) L3/4*sind(-220);L2+L3/4*cosd(-240) L3/4*sind(-240);L2+L3/4*cosd(-260) L3/4*sind(-260);L2+L3/4*cosd(-270) L3/4*sind(-270);L2+L3/4 L3/4;L2+L3/3+L3/3.2*cosd(30) L3/4+L3/3.2*sind(30);L2+L3/3+L3/3.2*cosd(26) L3/4+L3/3.2*sind(26);L2+L3/3+L3/8 L3/4;L2+L3/3+L3/4+L3/2*cosd(11) L3/8+L3/2*sind(11);L2+L3/3+L3/4+L3/2*cosd(9) L3/8+L3/2*sind(9);L2+L3/3+L3/4 L3/8;L2+L3/3+L3/4+L3/2*cosd(1) L3/2*sind(1);L2+L3/3+L3/4+L3/2*cosd(-1) L3/2*sind(-1);L2+L3/3+L3/4 0;L2+L3/3+L3/4+L3/2*cosd(0) -L3/8+L3/2*sind(0);L2+L3/3+L3/4+L3/2*cosd(-2) -L3/8+L3/2*sind(-2);L2+L3/3+L3/4 -L3/8;L2+L3/3+L3/4+L3/3*cosd(-2) -L3/4+L3/3*sind(-2);L2+L3/3+L3/4+L3/3*cosd(-4) -L3/4+L3/3*sind(-4);L2+L3/3+L3/4 -L3/4;L2+L3/4*cosd(-90) L3/4*sind(-90)]



B=[0 -L1] %此點為上手臂和下手臂的連結點 設此點當連結點便不會在關節處看到類似linshape的固定點 外型較美觀



m1=[cosd(theta1) sind(theta1);-sind(theta1) cosd(theta1)]; %為一旋轉theta1的旋轉矩陣



b=B*m1+[0 L1]%設B點轉動後為b點



Arm1=arm1(:,2)-L1



Ax1=arm1(:,1)*cosd(theta1)-Arm1(:,1)*sind(theta1)



%上手臂的旋轉



Ay1=arm1(:,1)*sind(theta1)+Arm1(:,1)*cosd(theta1)+L1patch(Ax1,Ay1,'r')



C=[L2 0]



%此點為下手臂和手掌的連結點 設此點當連結點便不會在關節處看到類似linshape的固定點



m2=[cosd(theta2) sind(theta2); -sind(theta2) cosd(theta2)];



%為一旋轉theta2的旋轉矩陣



c=C*m2 %設C點轉動後為c點



Ax2=arm2(:,1)*cosd(theta2)-arm2(:,2)*sind(theta2)+b(1)



%下手臂的旋轉



Ay2=arm2(:,1)*sind(theta2)+arm2(:,2)*cosd(theta2)+b(2)



patch(Ax2,Ay2,'m')



Palm=palm(:,1)-L2



Ax3=Palm(:,1)*cosd(theta3)-palm(:,2)*sind(theta3)+c(1)+b(1)



%手掌的旋轉



Ay3=Palm(:,1)*sind(theta3)+palm(:,2)*cosd(theta3)+c(2)+b(2)



patch(Ax3,Ay3,'g')



axis equal





5.1.3.
%theta1=90,theta2=-45,theta3=-30
%L1=30 L2=26 L3=18
輸入body(30,26,18,90,-45,-30)手臂尺寸輸入之圖

5.1.4.
模擬動畫
L1=30
L2=26
L3=18
function body2(L1,L2,L3,X1,X2,X3)
arm1=[0 -L1/5;L1/5*cosd(-80) L1/5*sind(-80);L1/5*cosd(-70) L1/5*sind(-70);L1/5*cosd(-60) L1/5*sind(-60);L1/5*cosd(-50) L1/5*sind(-50);L1/5*cosd(-40) L1/5*sind(-40);L1/4*cosd(-45) L1+L1/4*sind(-45);L1/4*cosd(-30) L1+L1/4*sind(-30);L1/4*cosd(-10) L1+L1/4*sind(-10);L1/4*cosd(10) L1+L1/4*sind(10);L1/4*cosd(30) L1+L1/4*sind(30);L1/4*cosd(45) L1+L1/4*sind(45);L1/4*cosd(60) L1+L1/4*sind(60);L1/4*cosd(75) L1+L1/4*sind(75);L1/4*cosd(90) L1+L1/4*sind(90);L1/4*cosd(105) L1+L1/4*sind(105); L1/4*cosd(120) L1+L1/4*sind(120);L1/4*cosd(135) L1+L1/4*sind(135);L1/4*cosd(150) L1+L1/4*sind(150);L1/4*cosd(170) L1+L1/4*sind(170);L1/4*cosd(190) L1+L1/4*sind(190);L1/4*cosd(210) L1+L1/4*sind(210);L1/4*cosd(225) L1+L1/4*sind(225);L1/5*cosd(220) L1/5*sind(220);L1/5*cosd(230) L1/5*sind(230);L1/5*cosd(240) L1/5*sind(240) ;L1/5*cosd(250) L1/5*sind(250);L1/5*cosd(260) L1/5*sind(260);L1/5*cosd(270) L1/5*sind(270)]

arm2=[L2/5*cosd(80) L2/5*sind(80);L2/5*cosd(90) L2/5*sind(90);L2/5*cosd(100) L2/5*sind(100);L2/5*cosd(120) L2/5*sind(120);L2/5*cosd(140) L2/5*sind(140);L2/5*cosd(160) L2/5*sind(160);L2/5*cosd(180) L2/5*sind(180);L2/5*cosd(-160) L2/5*sind(-160);L2/5*cosd(-140) L2/5*sind(-140);L2/5*cosd(-120) L2/5*sind(-120);L2/5*cosd(-100) L2/5*sind(-100);L2/5*cosd(-90) L2/5*sind(-90);L2/5*cosd(-80) L2/5*sind(-80);L2+L2/7*cosd(-100) L2/7*sind(-100);L2+L2/7*cosd(-90) L2/7*sind(-90);L2+L2/7*cosd(-70) L2/7*sind(-70);L2+L2/7*cosd(-50) L2/7*sind(-50);L2+L2/7*cosd(-30) L2/7*sind(-30);L2+L2/7*cosd(-10) L2/7*sind(-10);L2+L2/7*cosd(10) L2/7*sind(10);L2+L2/7*cosd(30) L2/7*sind(30);L2+L2/7*cosd(50) L2/7*sind(50);L2+L2/7*cosd(70) L2/7*sind(70);L2+L2/7*cosd(90) L2/7*sind(90);L2+L2/7*cosd(100) L2/7*sind(100);L2/5*cosd(80) L2/5*sind(80)]

palm=[L2+L3/4*cosd(-90) L3/4*sind(-90);L2+L3/4*cosd(-100) L3/4*sind(-100);L2+L3/4*cosd(-120) L3/4*sind(-120);L2+L3/4*cosd(-140) L3/4*sind(-140);L2+L3/4*cosd(-160) L3/4*sind(-160);L2+L3/4*cosd(-180) L3/4*sind(-180);L2+L3/4*cosd(-200) L3/4*sind(-220);L2+L3/4*cosd(-240) L3/4*sind(-240);L2+L3/4*cosd(-260) L3/4*sind(-260);L2+L3/4*cosd(-270) L3/4*sind(-270);L2+L3/4 L3/4;L2+L3/3+L3/3.2*cosd(30) L3/4+L3/3.2*sind(30);L2+L3/3+L3/3.2*cosd(26) L3/4+L3/3.2*sind(26);L2+L3/3+L3/8 L3/4;L2+L3/3+L3/4+L3/2*cosd(11) L3/8+L3/2*sind(11);L2+L3/3+L3/4+L3/2*cosd(9) L3/8+L3/2*sind(9);L2+L3/3+L3/4 L3/8;L2+L3/3+L3/4+L3/2*cosd(1) L3/2*sind(1);L2+L3/3+L3/4+L3/2*cosd(-1) L3/2*sind(-1);L2+L3/3+L3/4 0;L2+L3/3+L3/4+L3/2*cosd(0) -L3/8+L3/2*sind(0);L2+L3/3+L3/4+L3/2*cosd(-2) -L3/8+L3/2*sind(-2);L2+L3/3+L3/4 -L3/8;L2+L3/3+L3/4+L3/3*cosd(-2) -L3/4+L3/3*sind(-2);L2+L3/3+L3/4+L3/3*cosd(-4) -L3/4+L3/3*sind(-4);L2+L3/3+L3/4 -L3/4;L2+L3/4*cosd(-90) L3/4*sind(-90)]

for n=[1:10]
theta1=180-1.5*n
%上手臂旋轉-90度至-75度
theta2=-150+2.5*n
%下手臂旋轉-45度至-35度
theta3=-315-4.5*n
%手掌旋轉由-10度至-30度
B=[0 -L1]
%設此點用以當連結點(上手臂和下手臂)便不會在關節處看到類似linshape的固定點 外型較美觀
m1=[cosd(theta1) sind(theta1);-sind(theta1) cosd(theta1)];
b=B*m1+[0 L1]
Arm1=arm1(:,2)-L1
Ax1=arm1(:,1)*cosd(theta1)-Arm1(:,1)*sind(theta1)
Ay1=arm1(:,1)*sind(theta1)+Arm1(:,1)*cosd(theta1)+L1
patch(Ax1,Ay1,'r')
C=[L2 0]
%設此點用以當連結點(下手臂和手掌)便不會在關節處看到類似linshape的固定點 外型較美觀
m2=[cosd(theta2) sind(theta2); -sind(theta2) cosd(theta2)];
c=C*m2
Ax2=arm2(:,1)*cosd(theta2)-arm2(:,2)*sind(theta2)+b(1)
Ay2=arm2(:,1)*sind(theta2)+arm2(:,2)*cosd(theta2)+b(2)
patch(Ax2,Ay2,'m')
Palm=palm(:,1)-L2
Ax3=Palm(:,1)*cosd(theta3)-palm(:,2)*sind(theta3)+c(1)+b(1)
Ay3=Palm(:,1)*sind(theta3)+palm(:,2)*cosd(theta3)+c(2)+b(2)
patch(Ax3,Ay3,'g')
AXIS([-30 15 20 70])
%訂出範圍 則圖形在運轉時座標固定
pause(1.0)
end



5.2



5.2.1



手指關節在同一平面上移動時 有一運動連桿未與運動結相連可視為平面的三連桿開放型的運動鏈,有一運動連桿未與運動結相連在平面上手指上的三個結點均為自由度為1的旋轉對。手指可分三部分,將手指靠近掌的部分稱前端,接著中段,靠近指尖那段稱末端,前端從整個手掌攤平開始可向掌心部分轉動約90度(與手掌夾90度)。中段與前端夾角最大為90度,中段與末端夾角最大亦約90度。



使用古魯伯公式: m=3(N-J-1)+sum(fi)=3(4-3-1)+3=3,自由度為三。



5.2.2



function body(L1,L2,L4,X1,X2,X4) %將body function 的arm3修改後成arm4>



arm1=[0 -L1/5;L1/5*cosd(-80) L1/5*sind(-80);L1/5*cosd(-70) L1/5*sind(-70);L1/5*cosd(-60) L1/5*sind(-60);L1/5*cosd(-50) L1/5*sind(-50);L1/5*cosd(-40) L1/5*sind(-40);L1/4*cosd(-45) L1+L1/4*sind(-45);L1/4*cosd(-30) L1+L1/4*sind(-30);L1/4*cosd(-10) L1+L1/4*sind(-10);L1/4*cosd(10) L1+L1/4*sind(10);L1/4*cosd(30) L1+L1/4*sind(30);L1/4*cosd(45) L1+L1/4*sind(45);L1/4*cosd(60) L1+L1/4*sind(60);L1/4*cosd(75) L1+L1/4*sind(75);L1/4*cosd(90) L1+L1/4*sind(90);L1/4*cosd(105) L1+L1/4*sind(105); L1/4*cosd(120) L1+L1/4*sind(120);L1/4*cosd(135) L1+L1/4*sind(135);L1/4*cosd(150) L1+L1/4*sind(150);L1/4*cosd(170) L1+L1/4*sind(170);L1/4*cosd(190) L1+L1/4*sind(190);L1/4*cosd(210) L1+L1/4*sind(210);L1/4*cosd(225) L1+L1/4*sind(225);L1/5*cosd(220) L1/5*sind(220);L1/5*cosd(230) L1/5*sind(230);L1/5*cosd(240) L1/5*sind(240) ;L1/5*cosd(250) L1/5*sind(250);L1/5*cosd(260) L1/5*sind(260);L1/5*cosd(270) L1/5*sind(270)]



arm2=[L2/5*cosd(80) L2/5*sind(80);L2/5*cosd(90) L2/5*sind(90);L2/5*cosd(100) L2/5*sind(100);L2/5*cosd(120) L2/5*sind(120);L2/5*cosd(140) L2/5*sind(140);L2/5*cosd(160) L2/5*sind(160);L2/5*cosd(180) L2/5*sind(180);L2/5*cosd(-160) L2/5*sind(-160);L2/5*cosd(-140) L2/5*sind(-140);L2/5*cosd(-120) L2/5*sind(-120);L2/5*cosd(-100) L2/5*sind(-100);L2/5*cosd(-90) L2/5*sind(-90);L2/5*cosd(-80) L2/5*sind(-80);L2+L2/7*cosd(-100) L2/7*sind(-100);L2+L2/7*cosd(-90) L2/7*sind(-90);L2+L2/7*cosd(-70) L2/7*sind(-70);L2+L2/7*cosd(-50) L2/7*sind(-50);L2+L2/7*cosd(-30) L2/7*sind(-30);L2+L2/7*cosd(-10) L2/7*sind(-10);L2+L2/7*cosd(10) L2/7*sind(10);L2+L2/7*cosd(30) L2/7*sind(30);L2+L2/7*cosd(50) L2/7*sind(50);L2+L2/7*cosd(70) L2/7*sind(70);L2+L2/7*cosd(90) L2/7*sind(90);L2+L2/7*cosd(100) L2/7*sind(100);L2/5*cosd(80) L2/5*sind(80)]



arm4=[L2+L4/5*cosd(80) L4/5*sind(80);L2+L4/5*cosd(90) L4/5*sind(90);L2+L4/5*cosd(100) L4/5*sind(100);L2+L4/5*cosd(120) L4/5*sind(120);L2+L4/5*cosd(140) L4/5*sind(140);L2+L4/5*cosd(160) L4/5*sind(160);L2+L4/5*cosd(180) L4/5*sind(180);L2+L4/5*cosd(-160) L4/5*sind(-160);L2+L4/5*cosd(-140) L4/5*sind(-140);L2+L4/5*cosd(-120) L4/5*sind(-120);L2+L4/5*cosd(-100) L4/5*sind(-100);L2+L4/5*cosd(-90) L4/5*sind(-90);L2+L4/5*cosd(-80) L4/5*sind(-80);L2+L4+L4/7*cosd(-100) L4/7*sind(-100);L2+L4+L4/7*cosd(-90) L4/7*sind(-90);L2+L4+L4/7*cosd(-70) L4/7*sind(-70);L2+L4+L4/7*cosd(-50) L4/7*sind(-50);L2+L4+L4/7*cosd(-30) L4/7*sind(-30);L2+L4+L4/7*cosd(-10) L4/7*sind(-10);L2+L4+L4/7*cosd(10) L4/7*sind(10);L2+L4+L4/7*cosd(30) L4/7*sind(30);L2+L4+L4/7*cosd(50) L4/7*sind(50);L2+L4+L4/7*cosd(70) L4/7*sind(70);L2+L4+L4/7*cosd(90) L4/7*sind(90);L2+L4+L4/7*cosd(100) L4/7*sind(100);L2+L4/5*cosd(80) L4/5*sind(80)]



%L1,L2,L4分別為指頭三段靠近手掌 中段 末端指頭 的長度



%theta1,theta2,theta4 分別為各結點的角度



B=[0 -L1]



%設此點用以當連結點 便不會在關節處看到類似linshape的固定點 外型較美觀



m1=[cosd(theta1) sind(theta1);-sind(theta1) cosd(theta1)];







b=B*m1+[0 L1]Arm1=arm1(:,2)-L1



Ax1=arm1(:,1)*cosd(theta1)-Arm1(:,1)*sind(theta1)



%靠近手掌那段的旋轉



Ay1=arm1(:,1)*sind(theta1)+Arm1(:,1)*cosd(theta1)+L1



patch(Ax1,Ay1,'r')



C=[L2 0]



%設此點用以當連結點 便不會在關節處看到類似linshape的固定點 外型較美觀



m2=[cosd(theta2) sind(theta2); -sind(theta2) cosd(theta2)];



c=C*m2



Ax2=arm2(:,1)*cosd(theta2)-arm2(:,2)*sind(theta2)+b(1)



%中段的部分旋轉



Ay2=arm2(:,1)*sind(theta2)+arm2(:,2)*cosd(theta2)+b(2)patch(Ax2,Ay2,'m')



Arm4=arm4(:,1)-L2



Ax3=Arm4(:,1)*cosd(theta3)-arm4(:,2)*sind(theta3)+c(1)+b(1)



%指頭的旋轉



Ay3=Arm4(:,1)*sind(theta3)+arm4(:,2)*cosd(theta3)+c(2)+b(2)patch(Ax3,Ay3,'g')



axis equal



pause(1.0)



end



食指食指軌跡



L1=4 L2=2.5 L4=2



theta1=100-8.8*n theta2=20-9*n*2 theta3=25-9*n*3




中指中指軌跡



L1=4.5 L2=3 L4=2.5



theta1=100-9*n theta2=20-9.6*n*2 theta3=25-8.5*n*3




無名指無名指軌跡



L1=4 L2=2.7 L4=2.4



theta1=100-7.8*n theta2=20-9.5*n*2 theta3=25-9*n*3




小姆指小姆指軌跡



L1=3.5 L2=2 L4=1.5



theta1=100-9*n theta2=20-10*n*2 theta3=26-9.6*n*3




5.2.3.



設投出的球速為150km/hr由於投球動作的組成包括了跨步,扭腰,手臂,手腕等多項因素,在此僅做指頭的分析(假設只動到指頭)將食指(其餘指頭視為與食指相同)的運動情形,由右向左投擲,令球出手時的速度等於指尖速度。



指頭上各節之長度分別為[4.5 2.5 2]cm



角度(對原點逆時針為正)[90 125 130]度



由假設算出



角速度[.462 .458 .449]rad/s



角加速度 [.501 .486 .453]rad/s^2




dyad_draw之函式分析



紅色為各指節點之加速度,藍色為速度,綠色為合速度圖形如下



投球的分析圖