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mics equations of the parallel manipulator are derived using Kane method, according to the theory, the active forces are equal to inertial forces, the dynamics statespace equation can be written by τ +G (Θ) = M (Θ) Θ+ V (Θ, Θ) Θ ( 3) B 动力学模型 并联机器人的动力学方 程导出凯恩方法,根据理论,主动力等于惯性力,动态状态空间方程可以写的 τ +G (Θ) = M (Θ) Θ+ V (Θ, Θ) Θ ( 3) where M (Θ) is the 66 mass matrix, V (Θ, Θ ) is an 61 vector of centrifugal and Coriolis terms, G (Θ) is an 61 vector of gravity terms, τ is a 61 vector of generalized applied forces. 在 M( Θ)是 66质量矩阵, V( Θ, Θ)是一个 61向量的离心和科里奥利术语, G( Θ)是一个 61重力矢量, τ是 61 向量的广义力。 The applied forces τ is transformed from mechanism actuator forces, which is given by τ= JlT *Fa ( 4) 应用部队 τ转化机制的执行力,这是由 τ= JlT *Fa ( 4) where J l is a Jacobian 66 matrix of transformation between generalized velocity Θ of platform and protraction velocity l of hydraulic cylinders, and Fa is a 61 vector representing cylinder forces. J1是 雅可比矩阵 66之间转换的广义速度 Θ平台和牵引速度的液压缸, Fa是一个 61向量表示气缸的力量。 The gravity term, G (Θ) , contains gravitational constant g and generalized coordinate Θ , it depends only on Θ , which can be described as G (Θ) = G p [(Juc,ai*Jai) T mu .g+ (J dc,ai .J ai) T . m d .g)] ( 5) 重力, G( Θ),包含引力常数 G和广义坐标 Θ,只取决于它 Θ,可以描述为 G (Θ) = G p [(Juc,ai*Jai) T mu .g+ (J dc,ai .J ai) T . m d .g)] ( 5) where Gp is upper platform gravity item, G p = m p *(g,0) T , mp is the total mass of upper platform and load, and the 31 gravitational constant vector g = (0,0, g ) T , mu is the mass of piston, md is the mass of hydraulic cylinder, J uc,ai is a Jacobian 33 matrix of velocity transformation between upper joints and the piston center of mass, J dc,ai is a Jacobian 33 matrix of velocity transformation between generalized velocity Θ and the hydraulic cylinder center of mass, and J ai, is is a Jacobian 36 matrix of velocity transformation between generalized velocity and upper joints Gp是上 平台重力项, G p = m p *(g,0) T ,Mp 是英国总质量上平台和负载,以及 31重力常数 r g = (0,0, g ) T , Mu是 质量是活塞, Md 是 液压缸的质量,Juc, ai是一个 3雅可比矩阵之间的转换3速度上和活塞质量中心, Jdc, ai是一个33的 雅可比矩阵之间的速度变换广 义速度 Θ 和液压缸的质心, Jai, is 是 是一个 3雅可比矩阵之间的 6 速度变换广义速度和上接头 CONTROL DESIGN 控制设计 In 6DOF hydraulic driven parallel manipulator, PID controller is applied to achieve tracking control of platform extensively, which is called Joint Space (JS) control scheme. 在六自由度液压驱 动并联机器人, PID控制 可实现跟踪控制平台广泛,这是所谓的联合空间 ( JS)控制方案。 The JS uses mechanism inverse kinematics for puting desired cylinder length trajectories from desired Cartesian trajectories, see Fig. 2. JS 利用机构逆运动学计算所需的气缸长度轨迹所需的笛卡尔轨迹,见图 2。 Figure 2. Joint space control scheme for 6DOF hydraulic Parallel manipulator platform 图 2。 关节空间控制方案的六自由度液压并联机器人平台 The modelbased controller considered the dynamic characteristic of parallel manipulator embedded the forward kinematics, dynamic gravity item and 基于模型的控制器是动态特性的并联 机器人的运动学嵌入,动态重力项和反 inverse of transfer of servovalve control hydraulic cylinders and inverse of transpose of Jacobian matrix (J l T ) −1 in inner control loop, see Fig. 3 转移的伺服阀控制液压缸和逆,转置雅 可比矩阵 (J l T ) −1在内部控制回路中,见图 3 Figure 3. PD with gravity pensation control scheme for 6DOF hydraulic driven parallel manipulator 图 3。 PD与 具有重力补偿控制方案的六自由度液压驱动并联机器人 The developed controller is extended to modelbased control scheme allowing tracking of the reference inputs for platform 所设计的控制器扩展模型为基础的控制方案允许跟踪参考输入平台 Desired position vector of hydraulic cylinders and actual position vector of hydraulic cylinders are used as input mands of the controller, and the controller provides th。
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