Minimum Energy Trajectory Planning For Three Degree Of Freedom Of Delta Parallel Mechanism

The parallel robot has many advantages such as good dynamic performance,strong carrying capacity,high stablility and reliability.Because of its complementary relationship with serial robot in application and function effectively.Due to its excellent performance,Parallel robot is widely used in manufacturing,flight training,scientific experiments,entertainment,education,CNC machine tools and so on.In this paper,the mechanism,kinematics,dynamics,singularity,kinematics and trajectory planning of parallel manipulators are explored.On the basis of the domestic and international researche results,the researche methods of trajectory planning for parallel mechanism are reviewed.The main work is as follows:Firstly,in the Cartesian coordinate system,a simplified geometric model of parallel mechanism for parallel robot is established.According to the fundamental theory of kinematics,the forward and reverse motion model of kinematics are obtained,then the nonlinear dynamic equations described the relationship between moving platform and drive arms of the parallel mechanism are established,and the velocity Jacobian matrix is obtained.On the one hand,DELTA kinematics is programmed in the MATLAB software,a numerical example is calculated by the kinematics program.The program is tested to show the model is valid.on the other hand,A simulation experiment is made by combining with Cro/E and ADMAS software after the DELTA virtual prototype is obtained,a comparation of between the calculation results and the simulation results shows the correctness of the kinematic model of the parallel mechanism.Secondly,a complete parallel mechanism dynamic equation is established by using the principle of virtual work method,considering the complexity of solving the dynamic equations,it is necessary to simplify the complete dynamical equations.Through analysis and comparision the torque contribution of the moving platform,the drive arm and the driven arm,it decides to weaken the driven arm's influence to the overall system.Based on the equivalent quality distribution principle,the simplified rigid body dynamic model is obtained by distributing the driven arm's torque to the other parts.The singularity of the parallel mechanism is analysised by the Jacobian Matrix,and the singular constraints is obtained,the singularity of parallel mechanism can be avoided from structural optimal design and far away from singular position.Thirdly,a research on the motion planning and working space is done.The planning path should be continuously and smoothly,in the Cartesian space,some path points was interpolated between the initial point and the final point at the same interval,these points are transformed into drive angle in the joint space based on the inverse kinematics,then the cubic B spline function is used as the basic function to describe the driving angular displacement,and obtained the image results.Based on inverse displacement solution and the spatial hierarchical search method,An simulated experiment is conducted in the cylindrical space to obtain location map.Finally,the trajectory planning is carried out with energy optimization as the evaluation index.Considering the dynamics,kinematics,singularity and torque constraints,making the goal of find the trajectory of the minimum energy consumption in constant time from the initial point to final point,taking the time interval of each route as the design variables,then the minimum energy consumption trajectory function model of parallel robot was founded,the function model is a constrained optimization problem essentially,the Intelligent Particle Swarm Optimization Algorithm is introduced to solve nonlinear constrained optimization problem,in joint space,the cubic B spline function is used as the basic function to describe the driving angular displacement,An experiment by programming in MATLAB to find the minimum energy trajectory is conducted.