###### Abstract  
Kinematic accuracy is a crucial indicator for evaluating the performance of mechanisms. Low-mobility parallel mechanisms are examples of parallel robots that have been successfully employed in many industrial fields. Previous studies analyzing the kinematic accuracy analysis of parallel mechanisms typically ignore the randomness of each component of input error, leading to imprecise conclusions. In this paper, we use homogeneous transforms to develop the inverse kinematics models of an improved Delta parallel mechanism. Based on the inverse kinematics and the first-order Taylor approximation, a model is presented considering errors from the kinematic parameters describing the mechanism's geometry, clearance errors associated with revolute joints and driving errors associated with actuators. The response surface method is employed to build an explicit limit state function for describing position errors of the end-effector in the combined direction. As a result, a mathematical model of kinematic reliability of the improved Delta mechanism is derived considering the randomness of every input error component. And then, reliability sensitivity of the improved Delta parallel mechanism is analyzed, and the influences of the randomness of each input error component on the kinematic reliability of the mechanism are quantitatively calculated. The kinematic reliability and proposed sensitivity analysis provide a theoretical reference for the synthesis and optimum design of parallel mechanisms for kinematic accuracy. K 26 July 2  
then established a new continuous stiffness mapping model for the Delta parallel mechanism [11]. [PERSON] et al. studied analytical mechanics approaches in the dynamic modelling of the Delta mechanism. Four modelling methods were analyzed and compared: One based on the Principle of Virtual Work, two based on [PERSON]'s equations and one based on [PERSON]'s formalism [12]. [PERSON] utilized the kineto-elasto-dynamics and the finite element method to perform a mathematical dynamic model of a Delta robot with flexible links [13]. In order to obtain the best dexterity over its workspace, [PERSON], [PERSON], and [PERSON] optimized the spatial 3-DOF Delta parallel manipulator with a floating-point genetic algorithm [14]. [PERSON] proposed a multi-objective optimal design for the Delta robot based on kineto-elastostatic performances such as uniformity of the dexterity, largest regular workspace, highest global stiffness and reduced moving mass for the Delta robot [15]. [PERSON] and [PERSON] presented an optimal design for the geometric parameters of 3-P2(US) Delta parallel mechanism using harmony search algorithm [16]. The research on the kinematic accuracy of serial and parallel mechanisms has attracted significant interest [17; 18]. [PERSON] et al. presented an error modeling methodology that enables the tolerance design and kinematic calibration of 3-RSS Delta mechanism. The sensitivity analysis and kinematic calibration were also carried out to investigate the influence of source errors on the pose accuracy [19; 20]. By using a laser tracker as a measurement tool, [PERSON] et al. presented an iterative method to identify 18 geometric errors of the Delta parallel robot [21]. [PERSON] et al. analyzed the kinematic accuracy of a 3-DOF Delta parallel manipulator via both Jacobian and geometric error models [22]. [PERSON] et al. researched the influence of dimensional deviations, kinematic joints clearances and input errors introduced by the actuator on the positioning accuracy of the 3-DOF Delta parallel robots [23; 24; 25]. [PERSON] and [PERSON] Designed generalized parallel manipulators, and the position analysis of the GPM was carried out to evaluate the workspace and reveal the motion characteristics [26]. [PERSON] et al. researched the actuator input selection and optimization of the parallel mechanism, and evaluated the motion stability of each actuator [27]; [PERSON] et al.