[R] linear model with coefficient constraints

[Rnewb]

I would like to perform a regression like the one below:

lm(x ~ 0 + a1 + a2 + a3 + b1 + b2 + b3 + c1 + c2 + c3, data=data)

However, the data has the property that a1+a2+a3 = A, b1+b2+b3 = B, and
c1+c2+c3 = C, where A, B, and C are positive constants.  So there are two
extra degrees of freedom, and R handles this by producing NA for two of the
coefficients.  Instead, I would prefer to remove the degrees of freedom by
forcing constraints on the coefficients produced by the model. 
Specifically, I want

coeff(b1) + coeff(b2) + coeff(b3) = coeff(c1) + coeff(c2) + coeff(c3) = 0.

I could accomplish this by writing code to suitably shift the coefficients
after performing the basic regression above, but I'm hoping there's a better
way.  Is there?

thanks,
Rnewb
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