Abstract: It is difficult to establish Jacobian matrix and determine the coordinate frames of links for non-standard actuator.A new analytical method to establish the Jacobian matrix and determine the coordinate frames for joints and links are proposed in this paper.The proposed method made the positioning analysis of end-effector easier in space.At the same time, it is necessary to prove the effectiveness of the proposed method theoretically and verify the localization and configuration capabilities through simulations.First of all, forward kinematics model was set up based on a non-standard five Degree Of Freedom(5-DOF) actuator.A frame transformation is performed from base coordinate to end-effector coordinate.The relation between two adjacent joints is defined by a homogenous pose matrix.Secondly, the necessary and sufficient conditions for comprehensive localization are derived.They can guide the actuator to perform various tasks, such as tracking, assembly and autonomous grasping.A 5-DOF actuator is considered here as an example and this holds good for any N-DOF.Thirdly, inverse kinematics solutions are obtained by using artificial Neural Network(NN) based on back-propagation Multi-Layer Perceptron (MLP, multilayer perceptron NN) and are not unique.A unique solution using nonlinear minimization optimization is found.A NN based on supervisory learning method including three inputs, twenty neurons and five outputs has been used.Excitation function tansigmoid and linear excitation function pureline are in hidden and outer layers respectively.In Cartesian coordinate space, NN is trained by means of Levenberg Marquardt (LM) algorithm.The training sets used are Denav Hartenberg(DH) parameters and Cartesian coordinates.The weights are updated continuously which reduces the Mean Square Error(MSE) gradually.When MSE reaches the threshold set up, NN training will be terminated.After training, the test sets are used to examine the capability of NN.Fourthly, there are two evaluation functions viz., localization and cost functions.The localization function is defined to evaluate the positioning property of end-effector.At the same time, in task space, it will check whether the actuator has reached the target point along the direction needed or not.The cost function is defined to evaluate the kinematics configuration.There is a great relevance between cost function and Jacobian matrix.Velocity mapping from each joint to the end-effector was described by Jacobian matrix.So the cost function could give expression for kinematic configuration.At the end, simulations and experiments are conducted.The settings include industrial computer UNO₂184G, 5-DOF non-standard actuator, Windows 7, MATLAB2012a.Coordinate frames for each joint are established and D-H parameters are determined.Then relative pose matrix is obtained between each of the two adjacent joints.Initial end-effector pose is obtained following right multiplication rule.The end-effector space range is formed under each joint operation range.Then, simulation is performed using NN, obtained localization and cost functions.The following results are obtained.The rank of Jacobian matrix is equal to 5.Therefore, this actuator met necessary and sufficient conditions for comprehensive positioning.NN method for solving inverse kinematics has reduced the computational complexity compared to conventional method.There are 21 groups of solutions when positioning to(41.4, 89.0, 104.5).The optimal solution obtained is(21.61, 91.44, 135.52, 221.42, 0) according to localization function rule.The optimal solution obtained according to cost function rule is(21.61, 125.73, 108.42, 221.99.41, 0).NN accuracy is 89.9%(approximately) while conventional method is 87.5%.By approximate estimation, the errors for θ1, θ2, θ3, θ4 and θ5 are 3.7°, 3.1°, 3.5°, 3.3°and 4.5°respectively.NN used 1.2 seconds while conventional method completed in 0.9 seconds.Therefore, computation accuracy has improved by 20% and efficiency by 2.4%.If the system is linear, the conventional method is chosen when less demand in real-time.In contrast, if the system is nonlinear, new method proposed in this paper is chosen when more demand in real-time.The minimum value of localization function is 0.96.The maximum value of cost function is 4.0349×1014.These two parameters decide the comprehensive positioning and the kinematics configuration.From the results presented, it can be concluded that the non-standard actuator with MLP has better localization and optimal configuration.