Barycenter of the union of two parametric curves

Question

Let $\gamma_1:t\in[a,b]\rightarrow (x_1(t),y_1(t))\in \mathbb{R}^2$

and $\gamma_2:t\in[a,b]\rightarrow (x_2(t),y_2(t))\in \mathbb{R}^2$ two parametrized curves

what is the barycenter of the curve $\gamma=\gamma_1\cup\gamma_2$?