This video shows a 5-degrees-of-freedom (DoFs) planar parallel robot with a reconfigurable end-effector (EE) that has been designed and built for the experimental section of our paper . In the video, the robot is shown performing a number of example motions; the goal is to show both the robot capabilities and the effectiveness of the algorithms (devised in the cited paper) for solving the Direct and Inverse Kinematics Problems, as said algorithms have been implemented in the robot's control system.

In order, the video is divided in the following parts:

1. the EE translates along the \( x \) axis while keeping the same configuration (that is, the kinematic chain that defines the EE keeps the same joint angles and the internal DoFs of the EE are not used);
2. the EE rotates around the \( z \) axis, again with a constant configuration;
3. the robot moves from one solution of the Inverse Kinematics Problem to another (both solutions correspond to the same EE pose \( \pi \));
4. the robot moves through a Type-1 singularity configuration (that is, one where there are nonzero joint velocity vectors that correspond to zero EE velocity);
5. finally, the robot is applied to a grasping task: the EE uses its internal DoFs to reconfigure its shape in order to grab a ball at a first position and move it to a second position. This shows an example application of a fully-parallel robot with a reconfigurable platform such as the one presented here. 

A parallel robot with configurable platform (PRCP) is a special parallel mechanism in which the end-effector (EE) has internal Degrees-of-Freedom (DoFs). In most previous works, this is achieved by designing the EE as a closed-loop kinematic chain that can be reconfigured during the motion according to users’ needs.

One of the first examples of planar PRCPs was in ^[1], where the authors studied a planar 4-DoF gripper and optimized its design according to suitable kinematic indexes. In ^[2], the concept of PRCPs (both planar and spatial) was extended to a larger class of architectures and a general screw-theoretic framework was presented to compute the mobility of these mechanisms. In ^[3], a 4-DoF PRCP, designed for multi-finger gripping (with two contact points), was studied in terms of its kinematics and singularity analysis. More recently, a general synthesis method for PRCPs (some of which have a planar structure) was presented in ^[4].

In ^[5], Lambert and Herder presented a literature review on PRCPs and proposed general results on the singularity and mobility analysis of this class of robots; later, in ^[6], a general method was presented to derive the complete Jacobians of PRCPs through screw theory.

PRCPs’ predicted applications are where extra DoFs beyond those needed to position and orient the EE are required to interact with the environment: for instance, PRCPs can be employed when the robot has to grasp objects ^[1]. An alternative solution would be mounting a gripper on the EE of a conventional parallel robot, but the gripper and its motor increase the moving inertia of the EE, which reduces the dynamic performance of the robot. PRCPs, instead, have all the motors located on the robot base and their configurable EE can provide an integrated grasping functionality.

PRCPs were also applied in the design of haptic interfaces where the operator can interact with the robot through several contact points on the EE: this design can lead to a smoother experience of the virtual environment with respect to standard haptic systems ^[3]. Other proposed applications for PRCPs (not necessarily planar ones) are for robot surgery such as laparoscopy and for rehabilitation systems.