## 1 Introduction  
A cable-driven parallel robot (CDPR) is a new kind of parallel kinematic machine system that is driven by flexible cables [1]. The main structure of CDPRs consists of a base frame, a moving platform, a certain number of driving cables, and winch modules. Such a simple structure makes CDPRs convenient for quick assemblage and reconfiguration. Therefore, CDPRs become more flexible than other kinds of robots in changing themselves to adapt to new tasks and environments. Moreover, CDPRs also have some common characteristics of traditional parallel robots made by rigid links, such as fast moving speed, large payload capacity, high precision, and good structural stiffness [2; 3; 4]. In addition, CDPRs also have their own advantages such as low moving mass, large workspace, and low manufacturing cost. Because of these superior characteristics, CDPRs are widely used in disaster rescues, large space motion, microgravity simulation, flight simulator, virtual reality, rehabilitation, etc. [5; 6; 7; 8; 9; 10; 11; 12; 13]. Geometric calibration is obligated for any robot to improve the kinematic accuracy. Generally, geometric calibration methods can be classified into two types, i.e., with and without external measurements. The previous ones should use extra sensors or measuring systems, such as the inclinometer and the laser tracker to obtain the required measuring data [14; 15; 16]. The later ones do not need any external sensor or measuring equipment, while only using the internal information to complete the calibration; thus, these methods are also called auto-calibration or self-calibration methods [17; 18; 19; 20]. For traditional rigid-link robots including both serial and parallel ones, calibrations are usually done by manufacturers before the robots leave their factories. Once calibrated, these robots do not need calibration again for normal use. However, this is totally different for CDPRs. Since most CDPRs are assembled at the users' places and need reconfiguration for different tasks, calibration of CDPRs is usually needed in daily use. Therefore, auto-calibration/self-calibration methods are especially significant for CDPRs. A variety of methods have been proposed on the calibration of CDPRs. For example, [PERSON] et al. proposed a kinematic calibration methodology by using two inclinometers for 6-DOF CDPRs [14]. [PERSON] et al. used a triple-level spatial positioner to obtain measuring data for calibration [15]. An interval-based approach has been reported in [21], and measurements were achieved according to external equipment similarly. There are also some auto-/self-calibration method that have been proposed. [PERSON] and [PERSON] presented an auto-calibration method for overconstrained CDPRs using internal position and force sensors to achieve measurements [17]. A differential kinematic and force-based forward kinematics for CDPRs were introduced in [22]. [PERSON] et al. presented two novel self-calibration methods, based on incremental displacement and cable tension, respectively [18]. Some researchers have proposed a number of calibration methods for CDPRs. However, most of them need to be done with external measuring equipment, like laser trackers, inclinometers, spatial positioners, etc. [14; 15; 21]. For some self-calibration methods [17; 19], they are only proposed for some specific mechanism CDPRs, such as 6-DOF CDPRs driven by eight or seven cables. There is no general automatic self-calibration method that has been proposed for all kinds of redundant CDPRs so far. This paper proposes a general self-calibration method that is applicable for redundantly-actuated CDPRs (both suspended and non-suspended configurations). The encoders of the servo motors are used to obtain the driving cable lengths that are required by the calibration model. Compared to traditional calibration methods with external measurements, the proposed method uses the internal sensors of CDPRs to generate measuring data.