To solve the inverse kinematic problem of the serial robots with 6 degrees of freedom（ DOF） whose axes of the last three joints intersect at a point

a solution algorithm is proposed. This algorithm adopts the product of exponentials（ POE） method to establish the kinematic model

and the inverse kinematics are solved by adopting geometric and algebraic methods combined with the Paden-Kahan sub-problem. The application of geometric method is to obtain the points of intersection of motion trajectory of the first three joints

and then the solution is converted into the known Paden-Kahan sub-problem

which makes the geometric significance more clearer

more intuitive and greatly simplifies the calculation. Algebraic elimination method is used to cope with the fourth and fifth joints

which reduces the manual calculation by employing MATLAB and effectively avoids the error caused by complex calculations. Finally

a closed-form solution of inverse kinematics is determined. Correctness of proposed algorithm is validated by experiment the maximum pose error is calculated in the order of 10-12 magnitude

which is demonstrated to possess an extremely high precision.