This paper deals with the workspace transition of the 3-rRPS metamorphic parallel mechanism in Hyperboloid configuration. The 3-rRPS metamorphic parallel mechanism is composed of three rRPS legs in which rR joint is reconfigurable. The reconfigurable rR joint allows the moving platform to switch into different Hyperboloid configurations. Two reconfiguration strategies of the mechanism are discussed. In Hyperboloid configurations, the three revolute joint axes are skew and are not parallel to the same plane. These axes can be set with any value within 0° and 90°. By using algebraic geometry approach and Euler parametrization, the workspace of the mechanism is characterized. This workspace is defined as point reachable workspace of any point on the moving platform. The shape of the workspace changes depending on the value of joint parameter angle ϕ. The primary decomposition is computed and it reveals that the 3-rRPS metamorphic parallel mechanism in Hyperboloid configurations can perform 3-dof coupled motions in which the translational motions are completely dependent on the rotational motions.

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