This paper investigates kinematics and statics analysis of a 3-UPU robot in screw coordinates. According to the definition of a twist, both the angular velocity of a rigid body and the linear velocity of a point on it are expressed in screw components. We therefore establish the twist equation (TE) to calculate the position and posture of each joint. This equation can be applied directly to analyze the statics. According to the definition of a wrench, both the force and torque of the planar linkage are expressed in wrench components. As a result, we establish wrench equations (WE) to express the resultant action of a force system in one coordinate frame. With the definition of twist and wrench, we can associate the kinematics with statics by unit screws. Compared with the traditional Cartesian coordinate method, the WE is free from complex algebraic manipulation and convenient to obtain wrench matrix by Plücker coordinates of each wrench. Numerical calculation is applied to solve the kinematics which can conveniently obtain the position and posture of each joint in absolute coordinate. Six unknown variables can be solved with each equation of wrench which contain 3 forces and 3 torques. The kinematics and static analysis of the 3-UPU robot validate this method.
This paper investigates Newton-Euler dynamics in Plücker coordinates for a parallel robot. In classical mechanics, the Newton–Euler equations describe the dynamics of a rigid body by combining translations and rotations. In accordance to the definition of a screw, the angular velocity of a rigid body and its linear velocity at a point are represented in Plücker coordinates. With Plücker coordinates, we get the absolute displacement through numerical integration on the velocity solution and acceleration through numerical differential interpolation of velocity of each joint. The absolute accelerations and displacements calculated in kinematics are used to establish the force equation and toque equation directly. Since both the displacement and acceleration can be numerically expressed in terms of velocity of first order, the most prominent merit of the algorithm is that the dynamics can be iterated based on the velocities in Plücker coordinates including forward and inverse dynamics. The dynamics of a spatial 3-UPU parallel robot validates the algorithm. Although this paper only discusses the dynamics of 3-UPU parallel robot, it is also suited to developing numerical algorithms for kinematics and dynamics of a series mechanism and hybrid mechanism.
Kinetostatics of a robot is an essential component of robotic analysis that includes actuation distribution and torque control. The extant methods mainly include the static transfer formulae and force Jacobian matrix algorithms based on the Denavit-Hartenberg (D-H) method. They can calculate the joint driving torque, but there are some limitations. This paper proposes a kinetostatics approach for analyzing the driving torque of serial manipulators. The instantaneous work done by the external load is expressed with reciprocal screw. It is the key idea of the approach to derive the kinetostatics equation in screw form and determine the required torque at each joint. This methodology is straightforward for programming. Through kinetostatic analysis of some typical serial manipulators, this paper shows the process of establishing the kinetostatics of every joint to calculate the torque in Plücker coordinates. The general spatial manipulator was analyzed and the solution demonstrates the universality of the method presented in this paper. In addition, the kinetostatic analysis method applies to all kinds of serial manipulators.
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