However, with the increase of the complexity of the system, it will become very difficult to express and differentiate equations of the kinetic and potential energy. So, the Lagrange method is often used for dynamic modeling of complex systems. Lagrange method is based on the energy conservation of the mechanical system, which can avoid the calculation of complex internal forces of the object system. Its disadvantage is that eliminating the internal force of the system is very difficult, so it will be very hard to solve the dynamic model of the robot with complex mechanisms. It has clear physical meaning and can establish equations directly. Newton Euler method extends the Newton Euler equation of a single body to multi-body system. Lagrange method and Newton Euler method are two main methods to establish the dynamic model of the robot. However, the process of establishing kinematic model of robots with complex mechanisms using the Denavit–Hartenberg method is complicated and the solution is complex, especially for the solution of velocity and acceleration. Currently, the Denavit–Hartenberg method based on the homogeneous matrix is the most widely utilized method for its clear physical meaning and has been programmed. But when the mobile robot is analyzed, the screw theory method cannot be directly used and the virtual link technology is needed for a transformation. Among them, the homogeneous matrix method and the screw theory method are applied widely.
![kinematics and dynamics calculator kinematics and dynamics calculator](https://i.ebayimg.com/thumbs/images/g/~GwAAOSwes5fEa~J/s-l96.jpg)
The methods to establish kinematic model of robots mainly include vector method, quaternion method, screw theory method, homogeneous matrix method, and so on. Therefore, it greatly increases the difficulty of modeling and calculating the kinematic and dynamic models of their mechanisms. So, the expressions of the component’s pose, velocity, and acceleration in the complex mechanisms can become extremely complicated. Motions of components in the complex mechanisms often have coupling relationships. Parallel robots and hybrid robots often have complex structures and include complex mechanisms such as the closed-chain mechanism and the branch mechanism.
#KINEMATICS AND DYNAMICS CALCULATOR SERIAL#
The hybrid robot combines the advantages of the serial robot and the parallel robot. Compared with the serial robot, the parallel robot has higher stiffness, bearing capacity, and precision, but its workspace is limited. Robots are mainly divided into three types: serial robot, parallel robot, and hybrid robot. The establishment of robot kinematic and dynamic models is the basis of robot kinematic analysis, path planning, dynamic analysis, motion control, and so on. Robot dynamic model establishes the mapping relation between driving forces needed on joints and the angles or displacements of joints. Robot kinematic model establishes the mapping relation between the pose of the end-effector and the angles or displacements of joints. Industrial robots are usually composed of the base, the end-effector, and several links connected by joints. Then, the results of the numerical calculation are compared with the results of virtual prototype simulation in ADAMS to verify the correctness. As an example, the kinematic and dynamic model of the manipulator developed in our laboratory is established and a working process of it is numerically calculated. Therefore, the proposed modeling and calculation method of kinematics and dynamics of robots is especially suitable for robots with complex mechanisms. Calculating by the properties of the Lie group can reduce the calculation and model complexity, especially for calculating the velocity and acceleration, which reduces the calculation error and eases the calculation. Establishing the model with this method can obtain clear physical meaning and make the expressions uniform and easy to program, which is convenient for computer-aided calculation and parameterization. The Lagrange equation is expressed by the obtained kinematic parameter expressions.
![kinematics and dynamics calculator kinematics and dynamics calculator](https://image1.slideserve.com/2027396/kinematics-kinematic-equations-l.jpg)
The component’s velocity is derived using the relationship between the Lie group and Lie algebra, and the acceleration and Jacobian matrix are then derived on this basis.
![kinematics and dynamics calculator kinematics and dynamics calculator](https://getcalc.com/formula/physics/kinematic-viscosity.png)
Aiming at this issue, in this paper, the pose of the component in robots is represented by the Euclidean group and its subgroups with the proposed method. The kinematic and dynamic models of robots with complex mechanisms such as the closed-chain mechanism and the branch mechanism are often very complex and difficult to be calculated.