Robot dynamic model in vector formats y dc2 Pc2 1. M(q)ä+ c(q, à) + g(q) = u dei 92 Cx(q, q) = ġ"Cx(q)4 k-th component Pci of vector c k-th column T 1(ƏMK + of matrix M(q) Cx(q) : ƏM symmetric matrix! 91 = - 2 aq 2. M(q)ä +S(q,ġ)ġ + g(q) = U NOTE: the model is in the form NOT a factorization of c ¤(q, ġ, ä) = u as expected symmetric Skj(q, ġ) = 2 Cxij(q)qi by S is not unique! matrix
Robot dynamic model in vector formats y dc2 Pc2 1. M(q)ä+ c(q, à) + g(q) = u dei 92 Cx(q, q) = ġ"Cx(q)4 k-th component Pci of vector c k-th column T 1(ƏMK + of matrix M(q) Cx(q) : ƏM symmetric matrix! 91 = - 2 aq 2. M(q)ä +S(q,ġ)ġ + g(q) = U NOTE: the model is in the form NOT a factorization of c ¤(q, ġ, ä) = u as expected symmetric Skj(q, ġ) = 2 Cxij(q)qi by S is not unique! matrix
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Obtain the Lagrangian equations of the PR(prismatic+rotarary) manipulator in the figure. write in vector form. (use the kinetic and potential energy,angular and lineer velecoties-h-m1-m2-I1-I2-w for finding lagrange equations)
I want to see how the kinetic and potential energies obtained for each link are found.
(do not copy the answer from another answered question)
Transcribed Image Text:Robot dynamic model
in vector formats
y
VDIV
dcz
Pc2
1. М(q)ӑ + c(q, ӑ) + g(g) 3D и
92
Cx (q, à) = q* Cx(q)ġ
k-th component
of vector c
Pci
k-th column
T
ƏM
91
1 (ƏMR
of matrix M (q) C;(q) = ; +a)
symmetric
matrix!
CR(q)
2 aq
2. М(q)й + S(9,q)д + g(q) — и
NOTE:
the model
is in the form
NOT a
factorization of c
symmetric Skj (q, ġ) = > Cxij (q)4i
\by 5 is not unique!
(q, ġ, ä) = u
matrix
in general
as expected
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