Inverse Kinematic - SCARA Robot
MK ยท Wed Feb 29, 2012 11:42 pm
Hello,
I'm still working on the inverse kinematic problem.
For a scara robot I got the equation system (i.e. groebner bases) below.
Does SINGULAR provide functions in order to solve g1 ... g4 symbolically (e.g. (c(1) = ... ) ? Is there any chance for an example?
Many thanks, MK
g1:
(4*a(1)^2*x^2+4*a(1)^2*y^2)*c(1)^2+(-4*a(1)^3*x+4*a(1)*a(2)^2*x-4*a(1)*x^3-4*a(1)*x*y^2)*c(1)+(a(1)^4-2*a(1)^2*a(2)^2+2*a(1)^2*x^2-2*a(1)^2*y^2+a(2)^4-2*a(2)^2*x^2-2*a(2)^2*y^2+x^4+2*x^2*y^2+y^4),
g2:
(-2*a(1)*y)*s(1)+(-2*a(1)*x)*c(1)+(a(1)^2-a(2)^2+x^2+y^2),
g3:
(-a(2))*c(12)+(-a(1))*c(1)+(x),
g4:
(2*a(2)*y)*s(12)+(-2*a(1)*x)*c(1)+(a(1)^2-a(2)^2+x^2-y^2)
I'm still working on the inverse kinematic problem.
For a scara robot I got the equation system (i.e. groebner bases) below.
Does SINGULAR provide functions in order to solve g1 ... g4 symbolically (e.g. (c(1) = ... ) ? Is there any chance for an example?
Many thanks, MK
g1:
(4*a(1)^2*x^2+4*a(1)^2*y^2)*c(1)^2+(-4*a(1)^3*x+4*a(1)*a(2)^2*x-4*a(1)*x^3-4*a(1)*x*y^2)*c(1)+(a(1)^4-2*a(1)^2*a(2)^2+2*a(1)^2*x^2-2*a(1)^2*y^2+a(2)^4-2*a(2)^2*x^2-2*a(2)^2*y^2+x^4+2*x^2*y^2+y^4),
g2:
(-2*a(1)*y)*s(1)+(-2*a(1)*x)*c(1)+(a(1)^2-a(2)^2+x^2+y^2),
g3:
(-a(2))*c(12)+(-a(1))*c(1)+(x),
g4:
(2*a(2)*y)*s(12)+(-2*a(1)*x)*c(1)+(a(1)^2-a(2)^2+x^2-y^2)