We treat the planar frictionless motion induced by a starting pulse on a two-body system with four degrees of freedom consisting of two equal rods hinged together. A full discussion of all possible planar forceless motions is given, and the hyperelliptic functions are found to be necessary. A particular case, namely the asymptotic one, in its two kinematic variants (open/closed) is faced. It is ruled by the nonlinear differential equation $$\dot \varphi = sign\dot \varphi _0 \frac{{\sqrt {3Asin\varphi } }}{{\sqrt {(1 + 3cos^2 \varphi )(1 + 3sin^2 \varphi )} }},\varphi (0) = \varphi _0 ,$$ , whose integration provides a link between the time and the Lagrangian coordinate ϕ by means of elliptic integrals of I, II, and III kinds. The other (angle) coordinate θ has been drawn to quadratures by knowing ϕ.