Wildfires have increased in frequency and severity over the last few years due to climate change, and firefighting robots are emerging to assist in combating them. However, current firefighting robots mainly rely on wheels/tracks and often face significant mobility constraints in forest terrains. To improve motion in such environments, a new quadruped robot designed for both walking and tree-climbing in wildfire tasks has been proposed. The robot consists of two segments (rear and front) connected by a novel parallel-actuated cylindrical joint.This study presents the workspace analysis of a front leg while the rear segment remains attached to the tree trunk to enable gripping maneuvers. When both rear legs are fixed, the rear segment has three degrees of freedom (3 DoF), whose workspace WS is determined by propagating each point to its neighbors via Newton-Raphson. For each point in WS, 𝑛 random values are sampled for the 7-DoF that run from the rear segment to the front leg: 3 DoF provided by the C-joint and 4 DoF of the leg itself.Then, solving the forward kinematics for each sample yields a volume of reachable positions. This large workspace allows the leg to negotiate trunk irregularities (e.g., branches) during the climbing more efficiently than conventional wheel-based climbing robots, enhancing mobility in complex unstructured forest environments.