## 1 Introduction  
The external fixator is a well-established technique in distraction osteogenesis which stimulates the body's self-healing capacity to gradually form new tissue [1; 2]. The classical Ilicarov ring fixator has obtained good clinical results in correcting tibial deformities [3]. However, the configuration of the Ilicarov frame needs to be modified constantly, which is a very complex process, especially in the implementation of multiplane correction [4]. Taylor spatial frame (TSF) allows multiplane correction without modifying the configuration of the frame to achieve continuous stability [5]. Traditionally, clinicians complete the deformity correction by manually adjusting the rods of the external fixator according to the prescription and the number of adjustments is limited by the patient's compliance to about four daily steps [6]. Complicated manual adjustment leads to accumulated adjustment error and trajectory deviation. Adjusting the rod length of TSF in sequence will cause the trajectory of the bone end to reach five intermediate configurations before fully adjusting all the rods, which will make the actual trajectory deviate from the ideal correction trajectory [7].  
In general, the patient cannot check the current correction status and the remaining deformity in real-time and does not know whether the correction plan has been implemented on that day, which will lead to an unstable emotion and cause the patient to forget to implement the plan [8]. The trajectory deviation caused by the accumulated adjustment errors is also an issue in practical application. Once the trajectory deviation occurs, it is necessary to take an X-ray to reestablish the correction strategy, which will increase the patient's radiation exposure [9]. [PERSON] et al., developed a teleoperation robot system based on a removable series-parallel mechanism that can be used for acute correction of long bone fractures [10; 11]. However, deformity correction is based on the distraction osteogenesis to stimulate the body's self-healing capacities to gradually form new tissue, which requires the patient to wear the external fixator for a long time [1]. By mounting six rods on Iizarov rings, [PERSON] et al., developed the hexapod system which can plan and correct deformities with computer assistance [12]. Several researchers have described the advantages and precision of similar mechanisms [13; 14; 15]. However, they cannot reflect the deflection of the actual and the target trajectory during the correction, and there is no trajectory verification of the pre-operative correction trajectory. Meanwhile, the effect of the orientation of the distal bone end on bone trajectory has not been considered during the implementation of different correction strategies. Additionally, kinematics and mathematical derivations of the bone end trajectory and how to model the resulting bone shape for each correction strategy have rarely been studied under an external fixator.  
The range of motion (ROM) is a crucial indicator to assess the correction capability of the external fixator, which must have a sufficient ROM to accommodate the correction requirement of different indications; otherwise, the correction plan will not be carried out [16]. At present, clinicians evaluate the ROM of the external fixator only by investigating the individual displacement and angle capabilities [11; 12], instead of investigating the ROM from a three-dimensional perspective. A numerical searching method is provided to investigate the ROM to assist clinicians in more intuitively assessing the fixator's correction capability.  
An electromotor-driven parallel external fixator is developed for tibia deformity correction based on the Stewart platform. It allows automatic adjustment and gradual correction of the deformity, reducing the involvement of the patient. The preliminary trajectory verification experiments are carried out utilizing the artificial bone model to investigate the accuracy of the developed fixator system.