Research On Calculation Algorithm And Construction Of Static Space Stiffness Of Serial Robot

Human arm can adjust the stiffness of joints so that the end of the arm can have certain kind of compliance.Compared to human arm the serial robot arm still lacks this ability.Constructing static space stiffness character of end tool of the serial robot by changing the stiffness of joints becomes a train of thought.In this paper,according to this train of thought the main contents are:(1)The stiffness of one variable stiffness joint was reconstructed and the result shows the elastic deformation of the joint is also an important factor of the stiffness.Belt drive way and crank-link mechanism were presented to improve the stiffness adjustment characteristic of that joint and they do.For example,when the stiffness is equal to 10000 Nm/rad,the stiffness adjustment speeds are reduced by 52.3% and 32.2% respectively.(2)For the serial robot,one relation formula of force balances state of external forces and joint torques was given.The relationship was proved with derivation of equation,and the experimental result shows that it's accuracy is high.Based on this relation,A general method to solve the stiffness of a serial robot was proposed and it is called "compliance matrix algorithm".Simulation shows the compliance matrix obtained by this algorithm is good to reflect the stiffness of the end tool of serial robot.Combining existing research results and the compliance matrix results of this paper,the symmetry property and positive definiteness of the compliance matrix was summarized.Using an existing geometric definition of stiffness matrix,the stiffness of a 6-joints serial robot composed of conventional joints was calculated and the result is same with the existing result.(3)The force-linear displacement compliant axes and the torque-rotation displacement compliant axes were defined and their existence condition,properties,position vector,main classification were studied.Under certain conditions,for these two kinds of compliant axes,there will be a planar compliance center or a spatial compliance center.The two kinds of compliant axes are the inherent properties of the rigid body,and their position and direction don't change with different coordinate system and it was proved by the theoretical derivation.(4)Assuming the serial robot is in a fixed position,using basic equations of compliant axes and the range of joint compliance,the construction equations of the force-linear displacement compliant axes,the torque-rotation displacement compliant axes,the eigen compliant axes,the twist compliant axes,and the wrench compliant axes were given.Two examples of force-linear displacement compliant axes show the construction equations are available.The construction equations were transformed into a linear programming problem and the solution of the linear programming can directly judge whether the construction equation has valid solution.