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1、大作业：PUMA机器人1. 坐标系建立利用D-H参数法建立坐标系：2D-H参数表()()190-9000-160160200a2d2-225453 9090-a30-4522540-900-110170509000-1001006000-2662663. 正运动学推导3.1变换矩阵求取列各D-H变换矩阵如下： 注：为书写方面，本文中又由，利用Matlab进行符号运算，运行程序PUMAzhengyundongxue（程序详见附录）得：其中3.2变换矩阵验证3.2.1初步验证根据DH参数表中i的初始值，将其带入后得到末端执行器的坐标为px= -d2py=a2+d4+d6pz=a3与初始设定一致，因
2、此初步判断变换矩阵正确。3.2.2使用matlab机器人工具箱详细验证()()(m)(m)190-9000-160160200a2=0.4318d2=0.14909-225453 9090-a3=-0.020320-4522540-900d4=0.43307-110170509000-1001006000d6=0.05625-266266利用matlab机器人工具箱按照以上DH参数，编写并运行程序PUMAyanzheng（程序详见附录）得到如下图，与PUMA560机器人一致，表明DH参数法建模正确。 4. 逆运动学推导反变换法求逆，且有（1）求由 得 由矩阵对应元素均相等，得 得到：整理有三角
3、变换其中得到（2）求由得其中B3个元素如下：注：为书写方便，本文中。由矩阵元素对应相等， 得 两式平方求和，整理得到：其中，进行三角变换其中从而得到由，得解得（3）求（4）求由得解得（5）求由，得时，解得（6）求由，得时，解得5. 工作空间求取末端操作手的坐标为，根据正运动学推导结果，用Matlab编程求取其工作空间，根据参考文献获得PUMA560机器人各关节长度为：编写并运行程序PUMAgongzuokongjian（程序详见附录），得到：变换角度:俯视：综上，PUMA560运动的逆解可能存在8种。但是，由于结构的限制，例如各关节变量不能在全部360范围内运动，有着特定的范围，有些解不能实现
4、。这种多解情况下，应选取其中最满意的一组解，以满足机器人的工作要求。附录：（1） PUMAzhengyundongxue程序clearsyms a2 a3 d2 d4 d6 c1 c2 c3 c4 c5 c6 s1 s2 s3 s4 s5 s6;A1=c1 0 -s1 0;s1 0 c1 0;0 -1 0 0;0 0 0 1;A2=c2 -s2 0 a2*c2;s2 c2 0 a2*s2;0 0 1 d2;0 0 0 1;A3=c3 0 s3 -a3*c3;s3 0 -c3 -a3*s3;0 1 0 0;0 0 0 1;A4=c4 0 -s4 0;s4 0 c4 0;0 -1 0 d4;0 0
5、 0 1;A5=c5 0 s5 0;s5 0 -c5 0;0 1 0 0;0 0 0 1;A6=c6 -s6 0 0;s6 c6 0 0;0 0 1 d6;0 0 0 1;T60=A1*A2*A3*A4*A5*A6T60=subs(T60,c1 c2 c3 c4 c5 c6 s1 s2 s3 s4 s5 s6,0 1 0 1 1 1 1 0 1 0 0 0)（2） PUMAyanzheng程序clearL1=Link(-pi/2 0 0 0 0,standard)L2=Link(0 0.4318 0 0.14909 0,standard)L3=Link(pi/2 -0.02032 pi/2 0
6、 0,standard)L4=Link(-pi/2 0 0 0.43307 0,standard)L5=Link(pi/2 0 0 0 0,standard)L6=Link(0 0 0 0.05625 0,standard)r=robot(L1 L2 L3 L4 L5 L6 )drivebot(r)（3） PUMAgongzuokongjian程序cleara2=431.8;a3=20.32;d2=149.09;d4=433.07;d6=56.25;c1=-0.5*pi;c3=0.5*pi;c4=-0.5*pi;c5=0.5*pi;for b1=-160.*pi/180:32.*pi/180:
7、160.*pi/180for b2=-225.*pi/180:54.*pi/180:45.*pi/180for b3=-45.*pi/180:54.*pi/180:225.*pi/180for b4=-110.*pi/180:140.*pi/180:170.*pi/180for b5=-100.*pi/180:100.*pi/180:100.*pi/180 x=d4*(cos(b3)*sin(c3)*(cos(b1)*sin(b2) + cos(b2)*cos(c1)*sin(b1) +. sin(b3)*sin(c3)*(cos(b1)*cos(b2) - cos(c1)*sin(b1)*s
8、in(b2) + cos(c3)*sin(b1)*sin(c1) + . d6*(cos(c5)*(cos(c4)*(cos(b3)*sin(c3)*(cos(b1)*sin(b2) + cos(b2)*cos(c1)*sin(b1) + sin(b3)*sin(c3)*(cos(b1)*cos(b2) - cos(c1)*sin(b1)*sin(b2) + . cos(c3)*sin(b1)*sin(c1) + cos(b4)*sin(c4)*(cos(b3)*cos(c3)*(cos(b1)*sin(b2) + cos(b2)*cos(c1)*sin(b1) + cos(c3)*sin(b
9、3)*(cos(b1)*cos(b2) - . cos(c1)*sin(b1)*sin(b2) - sin(b1)*sin(c1)*sin(c3) + sin(b4)*sin(c4)*(cos(b3)*(cos(b1)*cos(b2) - cos(c1)*sin(b1)*sin(b2) - sin(b3)*(cos(b1)*sin(b2) + . cos(b2)*cos(c1)*sin(b1) + sin(b5)*sin(c5)*(cos(b4)*(cos(b3)*(cos(b1)*cos(b2) - cos(c1)*sin(b1)*sin(b2) - sin(b3)*(cos(b1)*sin
10、(b2) + . cos(b2)*cos(c1)*sin(b1) - sin(b4)*(cos(b3)*cos(c3)*(cos(b1)*sin(b2) + cos(b2)*cos(c1)*sin(b1) + cos(c3)*sin(b3)*(cos(b1)*cos(b2) - cos(c1)*sin(b1)*sin(b2) - . sin(b1)*sin(c1)*sin(c3) + cos(b5)*sin(c5)*(cos(b4)*cos(c4)*(cos(b3)*cos(c3)*(cos(b1)*sin(b2) + cos(b2)*cos(c1)*sin(b1) + cos(c3)*sin
11、(b3)*(cos(b1)*cos(b2) - . cos(c1)*sin(b1)*sin(b2) - sin(b1)*sin(c1)*sin(c3) - sin(c4)*(cos(b3)*sin(c3)*(cos(b1)*sin(b2) + cos(b2)*cos(c1)*sin(b1) + sin(b3)*sin(c3)*(cos(b1)*cos(b2) - . cos(c1)*sin(b1)*sin(b2) + cos(c3)*sin(b1)*sin(c1) + cos(c4)*sin(b4)*(cos(b3)*(cos(b1)*cos(b2) - cos(c1)*sin(b1)*sin
12、(b2) - sin(b3)*(cos(b1)*sin(b2) + . cos(b2)*cos(c1)*sin(b1) + a2*cos(b1)*cos(b2) + d2*sin(b1)*sin(c1) - a3*cos(b3)*(cos(b1)*cos(b2) - cos(c1)*sin(b1)*sin(b2) + a3*sin(b3)*(cos(b1)*sin(b2) + . cos(b2)*cos(c1)*sin(b1) - a2*cos(c1)*sin(b1)*sin(b2) y=d4*(cos(b3)*sin(c3)*(sin(b1)*sin(b2) - cos(b1)*cos(b2
13、)*cos(c1) + sin(b3)*sin(c3)*(cos(b2)*sin(b1) + cos(b1)*cos(c1)*sin(b2) - cos(b1)*cos(c3)*sin(c1) + . d6*(cos(c5)*(cos(c4)*(cos(b3)*sin(c3)*(sin(b1)*sin(b2) - cos(b1)*cos(b2)*cos(c1) + sin(b3)*sin(c3)*(cos(b2)*sin(b1) + cos(b1)*cos(c1)*sin(b2) - . cos(b1)*cos(c3)*sin(c1) + cos(b4)*sin(c4)*(cos(b3)*co
14、s(c3)*(sin(b1)*sin(b2) - cos(b1)*cos(b2)*cos(c1) + cos(c3)*sin(b3)*(cos(b2)*sin(b1) + . cos(b1)*cos(c1)*sin(b2) + cos(b1)*sin(c1)*sin(c3) + sin(b4)*sin(c4)*(cos(b3)*(cos(b2)*sin(b1) + cos(b1)*cos(c1)*sin(b2) - sin(b3)*(sin(b1)*sin(b2) - . cos(b1)*cos(b2)*cos(c1) + cos(b5)*sin(c5)*(cos(b4)*cos(c4)*(cos(b3)*cos(c3)*(sin(b1)*sin(b2) - cos(b1)*cos(b2)*cos(c1) + cos(c3)*sin(b
