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Repeated joints may be summarized by their number; so that joint notation for the SCARA robot can also be written 2RP for example. Joint notation for the parallel Gough-Stewart mechanism is 6-UPS or 6(UPS) indicating that it is composed of six identical serial limbs, each one composed of a universal U, active prismatic P and spherical S joint.
To determine the coordinate transformations [Z ] and [X ], the joints connecting the links are modeled as either hinged or sliding joints, each of which has a unique line S in space that forms the joint axis and define the relative movement of the two links. A typical serial robot is characterized by a sequence of six lines S i (i = 1, 2 ...
The connections between links are modeled as providing ideal movement, pure rotation or sliding for example, and are called joints. A linkage modeled as a network of rigid links and ideal joints is called a kinematic chain. Linkages may be constructed from open chains, closed chains, or a combination of open and closed chains.
In robotics, robot kinematics applies geometry to the study of the movement of multi-degree of freedom kinematic chains that form the structure of robotic systems. [1] [2] The emphasis on geometry means that the links of the robot are modeled as rigid bodies and its joints are assumed to provide pure rotation or translation.
Often links are presented as geometric objects, such as lines, triangles or squares, that support schematic versions of the joints of the mechanism or machine. [1] For example, the figures show the kinematic diagrams (i) of the slider-crank that forms a piston and crank-shaft in an engine, and (ii) of the first three joints for a PUMA manipulator.
A model of a robotic arm with joints. In robotics the common normal of two non-intersecting joint axes is a line perpendicular to both axes. [1]The common normal can be used to characterize robot arm links, by using the "common normal distance" and the angle between the link axes in a plane perpendicular to the common normal. [2]
Line representations in robotics are used for the following: They model joint axes: a revolute joint makes any connected rigid body rotate about the line of its axis; a prismatic joint makes the connected rigid body translate along its axis line. They model edges of the polyhedral objects used in many task planners or sensor processing modules.
An example of a simple open chain is a serial robot manipulator. These robotic systems are constructed from a series of links connected by six one degree-of-freedom revolute or prismatic joints, so the system has six degrees of freedom. An example of a simple closed chain is the RSSR spatial four-bar linkage.