- Serial manipulator
KUKArobots. In front is shown a 6-axis serial manipulator; behind it is a 4-axis palletizer.]
Serial manipulators are by far the most common industrial robots. Often they have an anthropomorphic mechanical arm structure, i.e. a serial chain of rigid links, connected by (mostly revolute) joints, forming a "shoulder", an "elbow", and a "wrist".
Their main advantage is their large
workspacewith respect to their own volume and occupied floor space.
Their main disadvantages are
* the low stiffness inherent to an open kinematic structure
* errors are accumulated and amplified from link to link
* the fact that they have to carry and move the large weight of most of the actuators
* the relatively low effective load that they can manipulate
rigid body motionit is known that it requires at least six degrees of freedom to place a manipulated object in an arbitrary position and orientation in the workspace of the robot. Hence, many serial robots have six joints.However the most popular application for serial robots in today's industry is pick-and-place assembly. Since this only requires four degrees of freedom, special assembly robots of the so called SCARAtype are built.
In its most general form, a serial robot consists of a number of rigid links connected with joints. Simplicity considerations in manufacturing and control have led to robots with only revolute or
prismatic joints and orthogonal, parallel and/or intersecting joint axes (instead of arbitrarily placed joint axes).
Donald L. Pieper derived the first practically relevant result in this context  , referred to as
321 kinematic structure:"The inverse kinematics of serial manipulators with six revolute joints, and with three consecutive joints intersecting, can be solved in closed-form, i.e. analytically"This result had a tremendous influence on the design of industrial robots.
The position and orientation of a robot's
end effectorare derived from the joint positions by means of a geometric model of the robot arm. For serial robots, the mapping from joint positions to end-effector pose is easy, the inverse mapping is more difficult. Therefore, most industrial robots have special designs that reduce the complexity of the inverse mapping.
The reachable workspace of a robot's end-effector is the manifold of reachable frames.
The dextrous workspace consists of the points of the reachable workspace where the robot can generate velocities that span the complete tangent space at that point, i.e., it can translate the manipulated object with three degrees of freedom, and rotate the object with three degrees of rotation freedom.
The relationships between joint space and Cartesian space coordinates of the object held by the robot are in general multiple-valued: the same pose can be reached by the serial arm in different ways, each with a different set of joint coordinates. Hence the reachabla workspace of the robot is divided in configurations (also called assembly modes), in which the kinematic relationships are locally one-to-one.
At a singularity the end-effector looses one or more degrees of twist freedom (instantaneously, the end-effector cannot move in these directions).
Serial robots with less than six independent joints are always singular in the sense that they can never span a six-dimensional twist space. This is often called an architectural singularity.A singularity is usually not an isolated point in the workspace of the robot, but a sub-manifold.
A manipulator with n joints is called redundant if it is used to perform a task that requires less than the available n degrees of freedom.
 D.L. Pieper. The kinematics of manipulators under computer control. PhD Thesis, Stanford University, Department of Mechanical Engineering, 1968
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