Introduction for modeling
A robotic manipulator is designed to perform a task in the 3-D space. The tool or end effector is required to follow a planned trajectory to manipulate objects or carry out the task in the workspace. This requires control of position of each link and joint of the manipulator to control both the position and orientation of the tool. To program the tool motion and joint-link motions, a mathematical model of the manipulator is required to refer to all geometrical and/or time-based properties of the motion. Kinematics model describes the spatial position of joints and links, and position and orientation of the end-effector. The derivatives of kinematics deal with the mechanics of motion without considering the forces that cause it. The relationships between the motions and the forces and/or torques that cause them is the dynamics problem.
In designing a robot manipulator, kinematics and dynamics play a vital role. The mathematical tools of spatial descriptions developed in the previous chapter are used in the modelling of robotic manipulators. The kinematics model gives relations between the position and orientation of the end-effectors and spatial positions of joint-links. The differential kinematics of manipulators refers to differential motion, that is, velocity, acceleration, and all higher order derivatives of position variables. The problem of completely describing the position and orientation of a manipulator, the kinematics model, is considered in this and the next chapter. Mechanical structure and notations
A manipulator consists of a chain of rigid bodies, called links, connected links each of which allow linear or revolute motion between conned links each of which exhibits just one degree of freedom (DOF). Joints with more than one (DOF) not
MODELING CHAPTER 3
- 3 -
common. A joint with m degrees of freedom cap one degree of freedom each connected with (m_1) links of zero length most industrial robotic manipulate are open serial kinematics chains that's each link is connected to two other links. at the most ,without the formation of closed loops In open chain robots all joints are motorized (active) Some Robots May Have Closed Kinematics chains Such as parallelogram linkages and require different Considerations to Them.
The number of degrees of freedom a manipulator possesses is the number of independent parameters required to completely specify its position and orientation in space. Because each joint has only one degrees of freedom. The degrees of freedom of a manipulator are equal to number of Joints.