| Summary: | Parallel robots with configurable platforms are a class of robots in which the end-effector has an inner mobility, so that its overall shape can be reconfigured: in most cases, the end-effector is thus a closed-loop kinematic chain composed of rigid links. These robots have a greater flexibility in their motion and control with respect to rigid-platform parallel architectures, but their kinematics is more challenging to analyze. In our work, we consider <i>n</i>-<span style="text-decoration: underline;">R</span>RR planar configurable robots, in which the end-effector is a chain composed of <i>n</i> links and revolute joints, and is controlled by <i>n</i> rotary actuators located on the base of the mechanism. In particular, we study the geometrical design of such robots and their direct and inverse kinematics for <inline-formula><math display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>4</mn></mrow></semantics></math></inline-formula>, <inline-formula><math display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>5</mn></mrow></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>6</mn></mrow></semantics></math></inline-formula>; we employ the bilateration method, which can simplify the kinematic analysis and allows us to generalize the approach and the results obtained for the 3-<span style="text-decoration: underline;">R</span>RR mechanism to <i>n</i>-<span style="text-decoration: underline;">R</span>RR robots (with <inline-formula><math display="inline"><semantics><mrow><mi>n</mi><mo>></mo><mn>3</mn></mrow></semantics></math></inline-formula>). Then, we study the singularity configurations of these robot architectures. Finally, we present the results from experimental tests that have been performed on a 5–<span style="text-decoration: underline;">R</span>RR robot prototype.
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