CAJ | 학술논문

在3-PRS并联机器人设计与控制过程中，求解其输入与末端位姿之间速度及加速度的传递关系是工作重点，但该解析表达式比较复杂。通过直接采用对时间求导数的方法，得到3-PRS并联机器人速度运动学的解析表达式。针对推导复杂的问题，利用MATLAB提供的符号推导函数，直接求得输入输出间速度与加速度关系表达式中矩阵的解析表达式；用替换函数将变量替换为具体的数值得到最终的数值解。给出了具体计算程序，最后用算例验证了该方法的可行性及程序的有效性。结果表明：采用MATLAB的符号推导功能，可以方便地用解析法及数值法对3-PRS的速度运动学进行研究。
재3-PRS병련궤기인설계여공제과정중，구해기수입여말단위자지간속도급가속도적전체관계시공작중점，단해해석표체식비교복잡。통과직접채용대시간구도수적방법，득도3-PRS병련궤기인속도운동학적해석표체식。침대추도복잡적문제，이용MATLAB제공적부호추도함수，직접구득수입수출간속도여가속도관계표체식중구진적해석표체식；용체환함수장변량체환위구체적수치득도최종적수치해。급출료구체계산정서，최후용산례험증료해방법적가행성급정서적유효성。결과표명：채용MATLAB적부호추도공능，가이방편지용해석법급수치법대3-PRS적속도운동학진행연구。
The transmission relationship of velocities and accelerations between the input parameter and end orientation of manip-ulator is one key task in design and control process of 3-PRS parallel robot,but the analytic expression is rather complex. The velocity kinematics analytic expression of 3-PRS parallel robot was gotten through directly using the method of differentiating with respect to time. Aiming at complexity problem of derivation,the analytic expression of matrixes in the expression of transmission relationship of velocities and accelerations between input and output was gotten directly using the symbolic derivation function provided in MATLAB. The final numerical solution was gotten by replacing all the variables with actual values by using replacing function. The detailed calcu-lation program was presented,and the feasibility of the method and the effectiveness of the program were verified through computing ex-amples finally. The result shows that using the symbolic derivation computation functions of MATLAB can facilitate study on velocity ki-nematics of 3-PRS parallel robot using analytic and numerical method.