Kinematics simulation of 6R mechanical arm based on MATLAB
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摘要: 为了更好地控制液压机械臂在工业生产中作业，以6R液压机械臂为研究对象，运用改进D-H法对其进行建模，建立正运动学方程，通过空间几何法和数值解析法结合的方式得到机械臂各关节角度变量的8组解。通过MATLAB软件中的Robots Toolbox对机械臂建模，在关节空间内对其进行运动轨迹仿真，得到各关节轴的角位移、角速度和角加速度随时间变化的平滑曲线，仿真结果验证了所建立的运动学方程的正确性以及该机械臂参数的合理性。为后续液压机械臂的运动规划及实时控制提供了必要的理论基础和正确的运动学模型。Abstract: In order to better control the operation of the hydraulic manipulator in industrial production, the 6R hydraulic manipulator is taken as the research object, the improved D-H method is used to model it, and the forward kinematics equation is established. Eight sets of solutions for the angle variables of each joint of the manipulator are obtained. The robotic arm is modeled by Robots Toolbox in MATLAB software, the motion trajectory of the robot was simulated in the joint space, and the smooth curves of angular displacement, angular velocity and angular acceleration of each joint axis with the time were obtained. The simulation results proved that the kinematics equation established is correct and the parameters of the robot are reasonable. It provides the necessary theoretical basis and correct kinematics model for the subsequent motion planning and real-time control of the hydraulic manipulator.
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Key words:
- six degree of freedom mechanical arm /
- MATLAB /
- kinematics /
- simulation
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表 1 液压机械臂D-H参数
$ i $ $ {a}_{i-1}/{\rm{mm}} $ ${\alpha _{i - 1} }/(^\circ )$ $ {d_i}/{\rm{mm}} $ ${\theta _i}/(^\circ )$ 关节范围/$ (^\circ ) $ 1 $ 0 $ $ 0 $ $ {d_1}(195) $ $ {\theta _1} $ $ (-120,120) $ 2 $ {a_1}(120) $ $ - 90 $ $ 0 $ $ {\theta _2} $ $ ( - 32.5,87.5) $ 3 $ {a_2}(850) $ $ 0 $ $ 0 $ $ {\theta _3} $ $ ( - 172,98) $ 4 $ {a_3}(500) $ $ 0 $ $ 0 $ $ {\theta _4} $ $ ( - 90,90) $ 5 $ {a_4}(130) $ $ 90 $ $ 0 $ $ {\theta _5} $ $ (-90,90) $ 6 $ 0 $ $ -90 $ $ {d_6}(80) $ $ {\theta }_{6} $ $ ( - 360,360) $ 
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表 2 运动学逆解数值
组别 $ {\theta _1} $ $ {\theta _2} $ $ {\theta _3} $ $ {\theta _4} $ $ {\theta _5} $ $ {\theta _6} $ 1 0.523 6 1.047 2 0.785 4 1.309 0 0.785 4 2.094 4 2 0.523 6 1.618 6 −0.785 4 −3.974 8 0.785 4 2.094 4 3 0.523 6 1.047 2 0.785 4 1.309 0 −0.785 4 2.094 4 4 0.523 6 1.618 6 −0.785 4 −3.974 8 −0.785 4 2.094 4 5 −2.618 0 1.858 2 0.342 9 −2.201 0 2.356 2 −1.047 2 6 −2.618 0 2.111 3 −0.342 9 −1.768 5 2.356 2 −1.047 2 7 −2.618 0 1.858 2 0.342 9 −2.201 0 −2.356 2 −1.047 2 8 −2.618 0 2.111 3 −0.342 9 −1.768 5 −2.356 2 −1.047 2
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