Abstract: The workspace dexterity of traditional robot is mainly solved by inverse kinematics (IK) method, which can not solve the workspace dexterity of collaborative robot because of the offset effect on the solution of inverse kinematics. So, an improved solving method without using the inverse kinematics is proposed. Firstly, the robot offset is defined and the deficiencies of the IK method are analyzed. Then, the geometric constraint satisfying the service point conditions is obtained with the service sphere, and the error model of dexterity is achieved by using the geometric constraint. Besides, the workspace dexterity index λ and the error parameter E which affect the dexterity solution are proposed. Then, the effects of parameters n, n₀ and n₁ on E and λ are analyzed in the improved method, and the values of the parameters are determined. Finally, through the comparison between the improved method and the IK method, it can be seen that the solution time of the improved method is shorter than the IK method and the computational efficiency is higher while guaranteeing the solution accuracy. The solving of the workspace dexterity of the collaborative robot with offset proves the strong adaptability of the improved method.