Motion generation systems are becoming increasingly important in certain Virtual Reality (VR) applications, such as vehicle simulators. This paper deals with the analysis of the Inverse Kinematics (IK) and the reachable workspace of a three-degrees-of-freedom (3-DOF) parallel manipulator, proposing different transformations and optimizations in order to simplify its use with Motion Cueing Algorithms (MCA) for self-motion generation in VR simulators. The proposed analysis and improvements are performed on a 3-DOF heave-pitch-roll manipulator with rotational motors, commonly used for low-cost motion-based commercial simulators. The analysis has been empirically validated against a real 3-DOF parallel manipulator in our labs using an optical tracking system. The described approach can be applied to any kind of 3-DOF parallel manipulator, or even to 6-DOF parallel manipulators. Moreover, the analysis includes objective measures (safe zones) on the workspace volume that can provide a simple but efficient way of comparing the kinematic capabilities of different kinds of motion platforms for this particular application.
IntroductionHuman-computer interactions can be really complex in simulation systems where a believable motion generation is needed for the fulfilment of the simulation goals. The use of motion platforms to add inertial cues can significantly enhance the user immersion in the simulator, provided the system is properly tuned (Casas et al., 2016;Nahon and Reid, 1990;Reid and Nahon, 1986). The understanding of motion platforms' behavior and functioning is necessary to design effective and immersive experiences with this kind of simulators. In this regard, there are several works in the literature focused on the analysis of the behavior of several motion mechanisms with different features. However, it is hard to find research works focused on the peculiarities of the usage of motion platforms for motion generation in real-time vehicle simulation, which is the main target of this contribution.One of the most important features of motion platforms when used in vehicle simulators is the amount of linear and angular displacement the device is able to provide over the different axes. These features are crucial since they can affect the physical validity of the simulator (Reymond and Kemeny, 2000) and enhance/reduce the magnitude distortion (Sinacori, 1977) of the generated perceptual cues. In consequence, they condition the experience of the simulators' users (Casas et al., 2015). These features are generally known in the literature as the workspace. This workspace can be expressed in terms of a Cartesian space or in terms of the amount of degrees-of-freedom (DOF) the manipulator is able to reach. For motion simulation, it is much more interesting to analyze it in terms of DOF-space due to the fact that motion platforms are usually designed based on the DOF, rather than in absolute positions.The goal of these motion platforms is to provide the user with the most suitable perception of driving/piloting the...