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-import solids;
-import tube;
-import graph3;
-import palette;
-size(8cm);
-
-currentprojection=perspective(
-camera=(13.3596389245356,8.01038090435314,14.4864483364785),
-up=(-0.0207054323419367,-0.00472438375047319,0.0236460907598947),
-target=(-1.06042550499095,2.68154529985845,0.795007562120261));
-
-defaultpen(fontsize(6pt));
-
-// draw coordinates and frames
-// axis1 is defined by z axis of TBase
-// axis2 is defined by z axis of TEnd
-void DrawFrame(transform3 TBase, transform3 TEnd, string s)
-{
- triple p1,v1,p2,v2;
- p1=TBase*O;
- v1=TBase*Z-p1;
- p2=TEnd*O;
- v2=TEnd*Z-p2;
- triple n=cross(v1,v2);
-
- real[][] A=
- {
- {v1.x,-v2.x,-n.x},
- {v1.y,-v2.y,-n.y},
- {v1.z,-v2.z,-n.z}
- };
-
- triple vb=p2-p1;
-
- real[] b={vb.x,vb.y,vb.z};
-
- // Get the extention along vector v1 and v2,
- // so, we can get the common normal between two axis
- real[] x=solve(A,b);
-
- real s1=x[0];
- real s2=x[1];
-
- // get foot of a perpendicular on both axies
- triple foot1=p1+s1*v1;
- triple foot2=p2+s2*v2;
-
- // draw two axis
- triple axis_a,axis_b;
- axis_a=p1+s1*v1*1.5;
- axis_b=p1-s1*v1*1.5;
- draw(axis_a--axis_b);
-
- axis_a=p2+s2*v2*1.5;
- axis_b=p2-s2*v2*1.5;
- draw(axis_a--axis_b);
-
- // draw "a"(common normal)
- draw(Label("$a_{"+s+"}$"),foot1--foot2,linewidth(1pt));
-
- // draw the coordinates frame
- triple dx,dy,dz,org;
- real length=0.8;
-
- org=foot1;
- dx =length*unit(foot2-foot1); // define the x axis of the frame on "a"
- dz =length*unit(v1); // define the z axis which is along axis1
- dy =length*unit(cross(dz,dx));
-
- draw(Label("$X_{"+s+"}$",1,align=-dy-dz),org--(org+dx),red+linewidth(1.5pt),
- Arrow3(8));
- draw(Label("$Y_{"+s+"}$",1,align=2dy-dz-dx),org--(org+dy),
- green+linewidth(1.5pt), Arrow3(8));
- draw(Label("$Z_{"+s+"}$",1,align=-2dx-dy),org--(org+dz),
- blue+linewidth(1.5pt), Arrow3(8));
-
- dot(Label("$O_{"+s+"}$",align =-dx-dz,black),org,black); // origin
-
-}
-
-void DrawLink(transform3 TBase, transform3 TEnd, pen objStyle,string s)
-{
- real h=1;
- real r=0.5;
- path3 generator=(0.5*r,0,h)--(r,0,h)--(r,0,0)--(0.5*r,0,0);
- revolution vase=revolution(O,generator,0,360);
- surface objSurface=surface(vase);
-
- render render=render(merge=true);
-
- // draw two cylinders
- draw(TBase*objSurface,objStyle,render);
- draw(TEnd*shift((0,0,-h))*objSurface,objStyle,render);
-
- // draw the link between two cylinders
- triple pStart=TBase*(0.5*h*Z);
- triple pEnd =TEnd*(-0.5*h*Z);
- triple pControl1=0.25*(pEnd-pStart)+TBase*(0,0,h);
- triple pControl2=-0.25*(pEnd-pStart)+TEnd*(0,0,-h);
- path3 p=pStart..controls pControl1 and pControl2..pEnd;
- draw(tube(p,scale(0.2)*unitsquare),objStyle,render);
-}
-
-// t1 and t2 define the starting frame and ending frame of the first link(i-1)
-transform3 t1=shift((0,0,1));
-transform3 t2=shift((0,0,-1))*rotate(-20,Y)*shift((0,3,2));
-// as, the two links were connected, so t2 is also the starting frame of link(i)
-// t3 defines the ending frame of link(i)
-transform3 t3=t2*rotate(40,Z)*shift((0,3,1.5))*rotate(-15,Y)*shift(-1.5*Z);
-
-// draw link(i-1)
-DrawLink(t1,t2,palegreen,"i-1");
-DrawFrame(t1,t2,"i-1");
-// draw link(i)
-DrawLink(t2,t3,lightmagenta,"i");
-DrawFrame(t2,t3,"i");
-
-
-// draw angle alpha, which is the angle between axis(i-1) and axis(i)
-triple p0=(0,0,-1);
-triple p1=(0,0,2.3);
-triple p2=shift((0,0,-1))*rotate(-20,Y)*(0,0,4);
-draw(p0--p2,cyan);
-draw("$\alpha_{i-1}$",arc(p0,p1,p2,Y,CW),ArcArrow3(3));
-
-
-// draw angle theta, which is the angle between a_i and a_{i-1}
-transform3 tx=shift((0,0,-1))*rotate(-20,Y)*shift((0,3,0));
-p0=tx*O;
-p1=tx*(0,3,0);
-p2=tx*rotate(40,Z)*(0,3,0);
-draw(p0--p1,cyan);
-draw(p0--p2,cyan);
-
-triple p1a=tx*(0,1.5,0);
-draw("$\theta_{i}$",arc(p0,p1a,p2),ArcArrow3(3));
-
-// draw d_{i-1}
-triple org_i =t2*shift((0,0,1.5))*O;
-draw(Label("$d_{i}$",0.13),p0--org_i,linewidth(1pt));