Abstract -- The process of modeling a series of hand-object parameters is crucial for precise and controllable robotic in-hand manipulation because it enables the mapping from the hand’s actuation input to the object’s motion to be obtained. Without assuming that most of these model parameters are known a priori or can be easily estimated by sensors, we focus on equipping robots with the ability to actively self-identify necessary model parameters using minimal sensing. Here, we derive algorithms, on the basis of the concept of virtual linkage-based representations (VLRs), to self-identify the underlying mechanics of hand-object systems via exploratory manipulation actions and probabilistic reasoning and, in turn, show that the self-identified VLR can enable the control of precise in-hand manipulation. To validate our framework, we instantiated the proposed system on a Yale Model O hand without joint encoders or tactile sensors. The passive adaptability of the underactuated hand greatly facilitates the self-identification process, because they naturally secure stable hand-object interactions during random exploration. Relying solely on an in-hand camera, our system can effectively self-identify the VLRs, even when some fingers are replaced with novel designs. In addition, we show in-hand manipulation applications of handwriting, marble maze playing, and cup stacking to demonstrate the effectiveness of the VLR in precise in-hand manipulation control.