Prismatic tensegrity structures represent a novel paradigm of robotic design, characterized by tensioned wires and compressed bars in a form of twisted prism with a fixed base and a flexible top. These structures present an alternative to classic stationary manipulators as they offer several advantages, such as stability of the system, lightweight construction, impact resistance, high payload capacity, and the ability to operate in unstructured environments. However, despite these benefits, prismatic tensegrity-based robot designs face challenges in areas such as the restricted horizontal workspace. To address this issue, this research letter proposes the first prismatic tensegrity manipulator with an active bar mechanism. The proposed robot aims to expand the workspace by adding reachability in the Z-axis. We simplify the control of the manipulator using a neural network. Furthermore, this study highlights the differences between classic active wire and novel active bar actuation mechanisms in tensegrity robot control. This article is organized as follows: robot design concept, research methodology, control strategy, experiments and results, and conclusions.