Cartesian parallel manipulators

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In robotics, Cartesian parallel manipulators are manipulators that move a platform using parallel-connected kinematic linkages ('limbs') lined up with a Cartesian coordinate system. Multiple limbs connect the moving platform to a base. Each limb is driven by a linear actuator and the linear actuators are mutually perpendicular. The term 'parallel' here refers to the way that the kinematic linkages are put together, it does not connote geometrically parallel; i.e., equidistant lines.

Contents

Context

Generally, manipulators (also called 'robots' or 'mechanisms') are mechanical devices that position and orientate objects. The position of an object in three-dimensional (3D) space can be specified by three numbers X, Y, Z known as 'coordinates.' In a Cartesian coordinate system (named after René Descartes who introduced analytic geometry, the mathematical basis for controlling manipulators) the coordinates specify distances from three mutually perpendicular reference planes.  The orientation of an object in 3D can be specified by three additional numbers corresponding to the orientation angles.  The first  manipulators were developed after World War II for the Argonne National Laboratory to safely handle highly radioactive material remotely.  The first numerically controlled manipulators (NC machines) were developed by Parsons Corp. and the MIT Servomechanisms Laboratory, for milling applications.  These machines position a cutting tool relative to a Cartesian coordinate system using three mutually perpendicular linear actuators (prismatic P joints), with (PP)P joint topology.  The first industrial robot, [1] Unimate, was invented in the 1950s. Its control axes correspond to a spherical coordinate system, with RRP joint topology composed of two revolute R joints in series with a prismatic P joint.  Most industrial robots today are articulated robots composed of a serial chain of revolute R joints RRRRRR.

Description

Cartesian parallel manipulators are in the intersection of two broader categories of manipulators: Cartesian and parallel. Cartesian manipulators are driven by mutually perpendicular linear actuators. They generally have a one-to-one correspondence between the linear positions of the actuators and the X, Y, Z position coordinates of the moving platform, making them easy to control. Furthermore, Cartesian manipulators do not change the orientation of the moving platform. Most commonly, Cartesian manipulators are serial-connected; i.e., they consist of a single kinematic linkage chain, i.e. the first linear actuator moves the second one and so on. On the other hand, Cartesian parallel manipulators are parallel-connected, i.e. they consist of multiple kinematic linkages. Parallel-connected manipulators have innate advantages [2] in terms of stiffness, [3] precision, [4] dynamic performance [5] [6] and in supporting heavy loads. [7]

Configurations

Various types of Cartesian parallel manipulators are summarized here. Only fully parallel-connected mechanisms are included; i.e., those having the same number of limbs as degrees of freedom of the moving-platform, with a single actuator per limb.

Multipteron family

Members of the Multipteron [8] family of manipulators have either 3, 4, 5 or 6 degrees of freedom (DoF). The Tripteron 3-DoF member has three translation degrees of freedom 3T DoF, with the subsequent members of the Multipteron family each adding a rotational R degree of freedom. Each member of the family has mutually perpendicular linear actuators connected to a fixed base. The moving platform is typically attached to the linear actuators through three geometrically parallel revolute R joints. See Kinematic pair for a description of shorthand joint notation used to describe manipulator configurations, like revolute R joint for example.

Tripteron

Tripteron Tripteron robot.jpg
Tripteron

The 3-DoF Tripteron [9] [10] [11] [12] [13] member of the Multipteron family has three parallel-connected kinematic chains consisting of a linear actuator (active prismatic P joint) in series with three revolute R joints 3(PRRR). Similar manipulators, with three parallelogram Pa limbs 3(PRPaR) are the Orthoglide [14] [15] and Parallel cube-manipulator. [16] The Pantepteron [17] is also similar to the Tripteron, with pantograph linkages to speed up the motion of the platform.

Qudrupteron

Quadrupteron Quadrupteron robot.jpg
Quadrupteron

The 4-DoF Qudrupteron [18] has 3T1R DoF with (3PRRU)(PRRR) joint topology.

Pentapteron

The 5-DoF Pentateron [19] has 3T2R DoF with 5(PRRRR) joint topology.

Hexapteron

The 6-DoF Hexapteron [20] has 3T3R DoF with 6(PCRS) joint topology, with cylindrical C and spherical S joints.

Isoglide

The Isoglide family [21] [22] [23] [24] includes many different Cartesian parallel manipulators from 2-6 DoF.

Xactuator

Xactuator Xactuator real hardware.jpg
Xactuator

The 4-DoF or 5-DoF Coupled Cartesian manipulators family [25] are gantry type Cartesian parallel manipulators with 2T2R DoF or 3T2R DoF.

Related Research Articles

<span class="mw-page-title-main">Machine</span> Powered mechanical device

A machine is a physical system using power to apply forces and control movement to perform an action. The term is commonly applied to artificial devices, such as those employing engines or motors, but also to natural biological macromolecules, such as molecular machines. Machines can be driven by animals and people, by natural forces such as wind and water, and by chemical, thermal, or electrical power, and include a system of mechanisms that shape the actuator input to achieve a specific application of output forces and movement. They can also include computers and sensors that monitor performance and plan movement, often called mechanical systems.

<span class="mw-page-title-main">Stewart platform</span> Type of parallel manipulator

A Stewart platform is a type of parallel manipulator that has six prismatic actuators, commonly hydraulic jacks or electric linear actuators, attached in pairs to three positions on the platform's baseplate, crossing over to three mounting points on a top plate. All 12 connections are made via universal joints. Devices placed on the top plate can be moved in the six degrees of freedom in which it is possible for a freely-suspended body to move: three linear movements x, y, z, and the three rotations.

<span class="mw-page-title-main">Inverse kinematics</span> Computing joint values of a kinematic chain from a known end position

In computer animation and robotics, inverse kinematics is the mathematical process of calculating the variable joint parameters needed to place the end of a kinematic chain, such as a robot manipulator or animation character's skeleton, in a given position and orientation relative to the start of the chain. Given joint parameters, the position and orientation of the chain's end, e.g. the hand of the character or robot, can typically be calculated directly using multiple applications of trigonometric formulas, a process known as forward kinematics. However, the reverse operation is, in general, much more challenging.

<span class="mw-page-title-main">Cartesian coordinate robot</span> Robot with axes of control that are linear and orthogonal

A Cartesian coordinate robot is an industrial robot whose three principal axes of control are linear and are at right angles to each other. The three sliding joints correspond to moving the wrist up-down, in-out, back-forth. Among other advantages, this mechanical arrangement simplifies the robot control arm solution. It has high reliability and precision when operating in three-dimensional space. As a robot coordinate system, it is also effective for horizontal travel and for stacking bins.

<span class="mw-page-title-main">Robot kinematics</span> Geometric analysis of multi-DoF kinematic chains that model a robot

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. 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.

<span class="mw-page-title-main">Linkage (mechanical)</span> Assembly of systems connected to manage forces and movement

A mechanical linkage is an assembly of systems connected to manage forces and movement. The movement of a body, or link, is studied using geometry so the link is considered to be rigid. 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.

<span class="mw-page-title-main">Delta robot</span>

A delta robot is a type of parallel robot that consists of three arms connected to universal joints at the base. The key design feature is the use of parallelograms in the arms, which maintains the orientation of the end effector. In contrast, Stewart platform can change the orientation of its end effector.

<span class="mw-page-title-main">Serial manipulator</span>

Serial manipulators are the most common industrial robots and they are designed as a series of links connected by motor-actuated joints that extend from a base to an end-effector. Often they have an anthropomorphic arm structure described as having a "shoulder", an "elbow", and a "wrist".

<span class="mw-page-title-main">Parallel manipulator</span>

A parallel manipulator is a mechanical system that uses several computer-controlled serial chains to support a single platform, or end-effector. Perhaps, the best known parallel manipulator is formed from six linear actuators that support a movable base for devices such as flight simulators. This device is called a Stewart platform or the Gough-Stewart platform in recognition of the engineers who first designed and used them.

In classical mechanics, a kinematic pair is a connection between two physical objects that imposes constraints on their relative movement (kinematics). German engineer Franz Reuleaux introduced the kinematic pair as a new approach to the study of machines that provided an advance over the motion of elements consisting of simple machines.

<span class="mw-page-title-main">Kinematic chain</span> Mathematical model for a mechanical system

In mechanical engineering, a kinematic chain is an assembly of rigid bodies connected by joints to provide constrained motion that is the mathematical model for a mechanical system. As the word chain suggests, the rigid bodies, or links, are constrained by their connections to other links. An example is the simple open chain formed by links connected in series, like the usual chain, which is the kinematic model for a typical robot manipulator.

<span class="mw-page-title-main">Robotic arm</span> Type of mechanical arm with similar functions to a human arm

A robotic arm is a type of mechanical arm, usually programmable, with similar functions to a human arm; the arm may be the sum total of the mechanism or may be part of a more complex robot. The links of such a manipulator are connected by joints allowing either rotational motion or translational (linear) displacement. The links of the manipulator can be considered to form a kinematic chain. The terminus of the kinematic chain of the manipulator is called the end effector and it is analogous to the human hand. However, the term "robotic hand" as a synonym of the robotic arm is often proscribed.

The Chebychev–Grübler–Kutzbach criterion determines the number of degrees of freedom of a kinematic chain, that is, a coupling of rigid bodies by means of mechanical constraints. These devices are also called linkages.

<span class="mw-page-title-main">Glossary of robotics</span> List of definitions of terms and concepts commonly used in the study of robotics

Robotics is the branch of technology that deals with the design, construction, operation, structural disposition, manufacture and application of robots. Robotics is related to the sciences of electronics, engineering, mechanics, and software.

<span class="mw-page-title-main">Mechanism (engineering)</span> Device used to transfer forces via non-electric means

In engineering, a mechanism is a device that transforms input forces and movement into a desired set of output forces and movement. Mechanisms generally consist of moving components which may include:

Kinematics equations are the constraint equations of a mechanical system such as a robot manipulator that define how input movement at one or more joints specifies the configuration of the device, in order to achieve a task position or end-effector location. Kinematics equations are used to analyze and design articulated systems ranging from four-bar linkages to serial and parallel robots.

<span class="mw-page-title-main">Hoberman mechanism</span> Mechanism that turns linear motion into radial motion

A Hoberman mechanism, or Hoberman linkage, is a deployable mechanism that turns linear motion into radial motion.

The product of exponentials (POE) method is a robotics convention for mapping the links of a spatial kinematic chain. It is an alternative to Denavit–Hartenberg parameterization. While the latter method uses the minimal number of parameters to represent joint motions, the former method has a number of advantages: uniform treatment of prismatic and revolute joints, definition of only two reference frames, and an easy geometric interpretation from the use of screw axes for each joint.

<span class="mw-page-title-main">Five-bar linkage</span> 2-DoF mechanism with 5 links and 5 joints

In kinematics, a five-bar linkage is a mechanism with two degrees of freedom that is constructed from five links that are connected together in a closed chain. All links are connected to each other by five joints in series forming a loop. One of the links is the ground or base. This configuration is also called a pantograph, however, it is not to be confused with the parallelogram-copying linkage pantograph.

A continuum robot is a type of robot that is characterised by infinite degrees of freedom and number of joints. These characteristics allow continuum manipulators to adjust and modify their shape at any point along their length, granting them the possibility to work in confined spaces and complex environments where standard rigid-link robots cannot operate. In particular, we can define a continuum robot as an actuatable structure whose constitutive material forms curves with continuous tangent vectors. This is a fundamental definition that allows to distinguish between continuum robots and snake-arm robots or hyper-redundant manipulators: the presence of rigid links and joints allows them to only approximately perform curves with continuous tangent vectors.

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