CAJ | 학술논문

为了有效地导出 Delta 机器人的解析解并实现运动控制，基于多体机械系统线性图论及其运动方程自动生成技术，将符号计算运用到 Delta 机器人上。首先建立了 Delta 机构的线性图解表达，利用符号计算引擎Maple 可对图解的约束方程进行数学描述，并最终求得了逆运动解的精确显式表达式，从而可直接地实现驱动控制和运动轨迹跟踪。用平面圆弧和 Adept 抓放2种实际工程的机械手运动模型，对 Delta 机器人的符号计算解进行了仿真分析。结果表明，用于 Delta 机器人驱动控制的符号解误差较小，满足快速运动的需求，从而确认了约束方程的运动学响应精度，并验证了显式符号解的正确性。
위료유효지도출 Delta 궤기인적해석해병실현운동공제，기우다체궤계계통선성도론급기운동방정자동생성기술，장부호계산운용도 Delta 궤기인상。수선건립료 Delta 궤구적선성도해표체，이용부호계산인경Maple 가대도해적약속방정진행수학묘술，병최종구득료역운동해적정학현식표체식，종이가직접지실현구동공제화운동궤적근종。용평면원호화 Adept 조방2충실제공정적궤계수운동모형，대 Delta 궤기인적부호계산해진행료방진분석。결과표명，용우 Delta 궤기인구동공제적부호해오차교소，만족쾌속운동적수구，종이학인료약속방정적운동학향응정도，병험증료현식부호해적정학성。
In order to effectively derive the inverse kinematic solution of the Delta robot and realize actuator control a description of the linear graph principle for automatically generating kinematic equations in a mechanical system as well as the symbolic computation implementation of this procedure is reviewed and projected into the Delta robot. Based on the established linear graph representation the explicit symbolic expression of constraint equations and inverse kinematic solutions are obtained successfully using a symbolic computation engine Maple so that actuator control and trajectory tracking can be directly realized.Two practical motions the circular path and Adept motion are simulated for the validation of symbolic solutions respectively.Results indicate that the simulation satisfies the requirement of the quick motion within an acceptable threshold. Thus the precision of kinematic response can be confirmed and the correctness of inverse solution is verified.