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The potential market of robots that can helpfully work at home is increasing, and such robots are required to possess force and tactile sensors achieving dynamic and cooperative interactions with their users. We proposed virtual force sensing (VFS) which, is a versatile solution allowing high spatial resolution and degrees of freedom instead of embedding force sensors in robots/machines. The technological key of the VFS is the estimation of the force, exerted by the user and applied to the robots/machines, by means of function approximation whose inputs are user's biological signals such as electromyogram (EMG) and postural information. In this study, we develop a three-dimensional force-vector estimator and investigate its performance through a three-dimensional trajectory tracing task. Experimental results demonstrate the feasibility of our approach.