Parallel robots
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This Chapter describes the common physical properties and the mathematical coordinate representations and algorithms, to work with the position, velocity and acceleration kinematics of parallel robots.
Parallel robots have a fundamentally different mechanical architecture than serial robots, as shown in this figure. The potential advantages of a parallel architecture are:
- Mechanical strength: the load at the end-effector is supported by multiple “legs” at the same time, resulting in lower forces per leg.
- Low moving mass: the motors of a typical parallel robot can all be placed on the fixed base (in contrast to the case of a typical serial robot), which significantly reduces the mass that must be moved.
Both aspects together lead to faster and lighter robots. However, this advantage also has a price:
- Smaller workspace: the workspace of a parallel robot is to a large extent constrained by the robot itself, i.e., by self-collisions between the legs.
- More complex mechanics: there are much more joints and links in a parallel robot than in an serial robot, making it more costly to construct, to maintain, and to achieve the same accuracy.
In industrial practice, the disadvantages seem to outweigh the advantages, except in the niche market of high-speed, low-accuracy motions with small loads.
Typical architecture of a parallel robot, with six identical
“legs” consisting of the serial connection of a Cardan joint
(two rotational degrees of freedom), a prismatic joint (one translational
degree of freedom), and a spherical joint (three rotational degrees of
freedom).
As with serial robots, most commercially successful parallel robots have special mechanical architectures, in order to make the kinematics algorithms as simple as possible. In addition, there exist a lot of dualities between the kinematics of serial and parallel robots:
- Force-velocity duality: the algorithms for the force transformations in a serial robot are formally very similar to the velocity transformations in a parallel robot, and vice versa.
- Forward-inverse duality: the forward kinematics of a serial robot is simple, while the inverse kinematics are difficult (in the sense that the equations to solve are non-linear and have multiple solutions); the opposite is true for a parallel robot.