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Let $T:ℝ/\mathbb{Z}\to ℝ/\mathbb{Z}$ be a von Neumann-Kakutani $q$- adic adding machine transformation and let $\varphi \in C^1\left(\right[0,1\left]\right)$. Put $${\varphi }_n\left(x\right):=\varphi \left(x\right)+\varphi \left(Tx\right)+...+\varphi (T^{n-1}x),x\in ℝ/\mathbb{Z},n\in \mathbb{N}.$$ We study three questions: 1. When will $\left({\varphi }_n\right(x){)}_{n\ge 1}$ be bounded? 2. What can be said about limit points of $\left({\varphi }_n\right(x){)}_{n\ge 1}?$ 3. When will the skew product $(x,y)\mapsto (Tx,y+\varphi (x\left)\right)$ be ergodic on $ℝ/\mathbb{Z}\times ℝ?$