Przykład 1

A=A1*A2*A3

A(1,1)=cos(p)*(cos(theta2var - p)*cos(p + theta1var) - sin(theta2var - p)*sin(p + theta1var)*cos(p)) - sin(p)*(sin(theta2var - p)*cos(p + theta1var) + cos(theta2var - p)*sin(p + theta1var)*cos(p))

A(1,2)= - cos(p)^2*(sin(theta2var - p)*cos(p + theta1var) + cos(theta2var - p)*sin(p + theta1var)*cos(p)) - cos(p)*sin(p)*(cos(theta2var - p)*cos(p + theta1var) - sin(theta2var - p)*sin(p + theta1var)*cos(p))

A(1,3)= cos(p)*sin(p)*(sin(theta2var - p)*cos(p + theta1var) + cos(theta2var - p)*sin(p + theta1var)*cos(p))

A(1,4)= a1*cos(p + theta1var) + a2*cos(theta2var - p)*cos(p + theta1var) - a2*sin(theta2var - p)*sin(p + theta1var)*cos(p)

A(2,1)= cos(p)*(cos(theta2var - p)*sin(p + theta1var) + sin(theta2var - p)*cos(p + theta1var)*cos(p)) - sin(p)*(sin(theta2var - p)*sin(p + theta1var) - cos(theta2var - p)*cos(p + theta1var)*cos(p))A(2,2)=

A(2,3)= - cos(p + theta1var)*sin(p)^2 - cos(p)^2*(sin(theta2var - p)*sin(p + theta1var) - cos(theta2var - p)*cos(p + theta1var)*cos(p)) - cos(p)*sin(p)*(cos(theta2var - p)*sin(p + theta1var) + sin(theta2var - p)*cos(p + theta1var)*cos(p))

A(2,4)= cos(p)*sin(p)*(sin(theta2var - p)*sin(p + theta1var) - cos(theta2var - p)*cos(p + theta1var)*cos(p)) - cos(p + theta1var)*cos(p)*sin(p)A(3,1)=

A(3,1)= cos(theta2var - p)*sin(p)^2 + sin(theta2var - p)*cos(p)*sin(p)

A(3,2)= cos(theta2var - p)*cos(p)^2*sin(p) - sin(theta2var - p)*cos(p)*sin(p)^2 + cos(p)*sin(p)

A(3,3)= cos(p)^2 - cos(theta2var - p)*cos(p)*sin(p)^2A(3,4)=

A(3,4)= d1 + a2*sin(theta2var - p)*sin(p)

A(4,1)=0

A(4,2)=0

A(4,3)=0

A(4,4)=1

Przykład 2

A(1,1)= cos(theta1var + 90)*cos(theta2var) - sin(theta1var + 90)*cos(180)*sin(theta2var)

A(1,2)= - cos(theta1var + 90)*sin(theta2var) - sin(theta1var + 90)*cos(180)*cos(theta2var)

A(1,3)=0

A(1,4)= a1*cos(theta1var + 90)

A(2,1)= sin(theta1var + 90)*cos(theta2var) + cos(theta1var + 90)*cos(180)*sin(theta2var)

A(2,2)= cos(theta1var + 90)*cos(180)*cos(theta2var) - sin(theta1var + 90)*sin(theta2var)

A(2,3)= -cos(theta1var + 90)*sin(180)

A(2,4)= a1*sin(theta1var + 90) - d2*cos(theta1var + 90)*sin(180)

A(3,1)=0

A(3,2)= sin(180)*cos(theta2var)

A(3,3)=0

A(3,4)= d1var + d2*cos(180)

A(4,1)=0

A(4,2)=0

A(4,3)=0

A(4,4)=1

Przykład 3

A(1,1)= cos(theta1var + 90)*cos(theta2var) - sin(theta1var + 90)*cos(180)*sin(theta2var)

A(1,2)= - cos(theta1var + 90)*sin(theta2var) - sin(theta1var + 90)*cos(180)*cos(theta2var)

A(1,3)=0

A(1,4)= a1*cos(theta1var + 90)

A(2,1)= sin(theta1var + 90)*cos(theta2var) + cos(theta1var + 90)*cos(180)*sin(theta2var)

A(2,2)= cos(theta1var + 90)*cos(180)*cos(theta2var) - sin(theta1var + 90)*sin(theta2var)

A(2,3)= -cos(theta1var + 90)*sin(180)

A(2,4)= a1*sin(theta1var + 90) - d2*cos(theta1var + 90)*sin(180)

A(3,1)=0

A(3,2)= sin(180)*cos(theta2var)

A(3,3)=0

A(3,4)= d1 + d2*cos(180)

A(4,1)=0

A(4,2)=0

A(4,3)=0

A(4,4)=1

Przykład 4

A(1,1)= cos(90)*(cos(theta4var)*(cos(theta1var + 90)*cos(theta3var) - sin(theta1var + 90)*sin(theta3var)) - sin(theta4var)*(cos(theta1var + 90)*sin(theta3var) + sin(theta1var + 90)*cos(theta3var))) + sin(90)*(cos(theta4var)*(cos(theta1var + 90)*sin(theta3var) + sin(theta1var + 90)*cos(theta3var)) + sin(theta4var)*(cos(theta1var + 90)*cos(theta3var) - sin(theta1var + 90)*sin(theta3var)))

A(1,2)= -sin(theta1var + 90)

A(1,3)=0

A(1,4)= a1var*cos(theta1var + 90) + a2*cos(theta1var + 90) - a4*sin(theta4var)*(cos(theta1var + 90)*sin(theta3var) + sin(theta1var + 90)*cos(theta3var)) + a3*cos(theta1var + 90)*cos(theta3var) - a3*sin(theta1var + 90)*sin(theta3var) + a4*cos(theta4var)*(cos(theta1var + 90)*cos(theta3var) - sin(theta1var + 90)*sin(theta3var))

A(2,1)= cos(90)*(cos(theta4var)*(cos(theta1var + 90)*sin(theta3var) + sin(theta1var + 90)*cos(theta3var)) + sin(theta4var)*(cos(theta1var + 90)*cos(theta3var) - sin(theta1var + 90)*sin(theta3var))) - sin(90)*(cos(theta4var)*(cos(theta1var + 90)*cos(theta3var) - sin(theta1var + 90)*sin(theta3var)) - sin(theta4var)*(cos(theta1var + 90)*sin(theta3var) + sin(theta1var + 90)*cos(theta3var)))

A(2,2)= cos(theta1var + 90)

A(2,3)=0

A(2,4)= a1var*sin(theta1var + 90) + a2*sin(theta1var + 90) + a4*sin(theta4var)*(cos(theta1var + 90)*cos(theta3var) - sin(theta1var + 90)*sin(theta3var)) + a3*cos(theta1var + 90)*sin(theta3var) + a3*sin(theta1var + 90)*cos(theta3var) + a4*cos(theta4var)*(cos(theta1var + 90)*sin(theta3var) + sin(theta1var + 90)*cos(theta3var))

A(3,1)= sin(90)*(cos(theta3var)*cos(theta4var) - sin(theta3var)*sin(theta4var)) - cos(90)*(cos(theta3var)*sin(theta4var) + cos(theta4var)*sin(theta3var))

A(3,2)=0

A(3,3)=0

A(3,4)= d1var + d2 - a3*sin(theta3var) - a4*cos(theta3var)*sin(theta4var) - a4*cos(theta4var)*sin(theta3var)

A(4,1)=0

A(4,2)=0

A(4,3)=0

A(4,4)=1

Przykład 5

A(1,1)= cos(theta1var + 90)*sin(theta2var - 90)*cos(90) + cos(theta2var - 90)*sin(theta1var + 90)*cos(90)^2

A(1,2)= -cos(theta2var - 90)*sin(theta1var + 90)*cos(90)*sin(90)

A(1,3)=0

A(1,4)= a3*(cos(theta1var + 90)*cos(theta2var - 90) - sin(theta1var + 90)*sin(theta2var - 90)*cos(90)) + a1*cos(theta1var + 90) - d3var*cos(theta2var - 90)*sin(theta1var + 90)*cos(90)*sin(90)

A(2,1)= sin(theta1var + 90)*sin(theta2var - 90)*cos(90) - cos(theta1var + 90)*sin(90)^2 - cos(theta1var + 90)*cos(theta2var - 90)*cos(90)^2A(2,2)=

A(2,2)= cos(theta1var + 90)*cos(theta2var - 90)*cos(90)*sin(90) - cos(theta1var + 90)*cos(90)*sin(90)

A(2,3)=0

A(2,4)= a1*sin(theta1var + 90) - d3var*(cos(theta1var + 90)*cos(90)*sin(90) - cos(theta1var + 90)*cos(theta2var - 90)*cos(90)*sin(90)) + a3*(cos(theta2var - 90)*sin(theta1var + 90) + cos(theta1var + 90)*sin(theta2var - 90)*cos(90))

A(3,1)= cos(90)*sin(90) - cos(theta2var - 90)*cos(90)*sin(90)A(3,2)=

A(3,2)= cos(theta2var - 90)*sin(90)^2 + cos(90)^2

A(3,3)=0

A(3,4)= d1var + d3var*(cos(theta2var - 90)*sin(90)^2 + cos(90)^2) + a3*sin(theta2var - 90)*sin(90)

A(4,1)=0

A(4,2)=0

A(4,3)=0

A(4,4)=1