Five-bar linkage

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Closed-Chain Five bar mechanism.png
Closed-Chain Geared Five bar mechanism.png
2 DOF five-bar mechanism with two input angles θ1 and θ2 and a geared mechanism, where the two disks represent meshing gears which are fixed to their corresponding links

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. [1] This configuration is also called a pantograph, [2] [3] however, it is not to be confused with the parallelogram-copying linkage pantograph.

Contents

The linkage can be a one-degree-of-freedom mechanism if two gears are attached to two links and are meshed together, forming a geared five-bar mechanism. [1]

Animation of a five-bar mechanism angle sweep over its workspace, done on MATLAB. The red arrow indicates the velocity direction of the end-effector due to unit speed input at the left motor and its length is proportional to its speed. Five-bar linkage animation.gif
Animation of a five-bar mechanism angle sweep over its workspace, done on MATLAB. The red arrow indicates the velocity direction of the end-effector due to unit speed input at the left motor and its length is proportional to its speed.

Robotic configuration

When controlled motors actuate the linkage, the whole system (a mechanism and its actuators) becomes a robot. [4] This is usually done by placing two servomotors (to control the two degrees of freedom) at the joints A and B, controlling the angle of the links L2 and L5. L1 is the grounded link. In this configuration, the controlled endpoint or end-effector is the point D, where the objective is to control its x and y coordinates in the plane in which the linkage resides. The angles theta 1 and theta 2 can be calculated as a function of the x,y coordinates of point D using trigonometric functions. This robotic configuration is a parallel manipulator. It is a parallel configuration robot as it is composed of two controlled serial manipulators connected to the endpoint.

Unlike a serial manipulator, this configuration has the advantage of having both motors grounded at the base link. As the motor can be quite massive, this significantly decreases the total moment of inertia of the linkage and improves backdrivability for haptic feedback applications. On the other hand, workspace reached by the endpoint is usually significantly smaller than that of a serial manipulator.

Velocity ellipses of a five-bar linkage robot. Velocity ellipses of a five-bar linkage robot.png
Velocity ellipses of a five-bar linkage robot.

Kinematics and dynamics

Both the forward and inverse kinematics of this robotic configuration can be found in closed-form equations through geometric relationships. Different methods of finding both have been done by Campion and Hayward. [2] Dynamic modeling of this robotic configuration has been done by Khalil and Abu Seif, [5] forming an equations of motion relating the torques applied at motor with the angles at the joints. The model assumes all links are rigid with center of gravity at their centers, and zero-stiffness at all joints.

Applications

This robotic linkage is used in many different fields ranging from prosthetics to haptic feedback. This design has been explored in several haptic feedback devices for general force feedback. [3] [2] It has also been used in the automatic drawing toy WeDraw. [6] A novel Ackermann-type steering mechanism design by Zhao et al. utilized a five-bar linkage instead of the regular four-bar linkage. [7] A prosthetic ankle-foot by Dong et al. used a geared five-bar spring mechanism to simulate the stiffness and damping behavior of a real foot. [1]

Related Research Articles

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

A machine is a physical system that uses 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">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">Four-bar linkage</span> Mechanical linkage consisting of four links connected by joints in a loop

In the study of mechanisms, a four-bar linkage, also called a four-bar, is the simplest closed-chain movable linkage. It consists of four bodies, called bars or links, connected in a loop by four joints. Generally, the joints are configured so the links move in parallel planes, and the assembly is called a planar four-bar linkage. Spherical and spatial four-bar linkages also exist and are used in practice.

<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 so as 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.

In physics, the degrees of freedom (DOF) of a mechanical system is the number of independent parameters that define its configuration or state. It is important in the analysis of systems of bodies in mechanical engineering, structural engineering, aerospace engineering, robotics, and other fields.

<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> Type of mechanical system

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.

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<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.

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A straight-line mechanism is a mechanism that converts any type of rotary or angular motion to perfect or near-perfect straight-line motion, or vice versa. Straight-line motion is linear motion of definite length or "stroke", every forward stroke being followed by a return stroke, giving reciprocating motion. The first such mechanism, patented in 1784 by James Watt, produced approximate straight-line motion, referred to by Watt as parallel motion.

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

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<span class="mw-page-title-main">Mechanism (engineering)</span> Device which converts input forces and motion to output forces and motion

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 Gears and gear trains; Belts and chain drives; cams and followers; Linkages; Friction devices, such as brakes or clutches; Structural components such as a frame, fasteners, bearings, springs, or lubricants; Various machine elements, such as splines, pins, or keys.

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<span class="mw-page-title-main">Jansen's linkage</span> Planar leg mechanism

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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">Leg mechanism</span> Mechanical system that walks

A leg mechanism is a mechanical system designed to provide a propulsive force by intermittent frictional contact with the ground. This is in contrast with wheels or continuous tracks which are intended to maintain continuous frictional contact with the ground. Mechanical legs are linkages that can have one or more actuators, and can perform simple planar or complex motion. Compared to a wheel, a leg mechanism is potentially better fitted to uneven terrain, as it can step over obstacles.

In mechanical engineering, kinematic synthesis determines the size and configuration of mechanisms that shape the flow of power through a mechanical system, or machine, to achieve a desired performance. The word synthesis refers to combining parts to form a whole. Hartenberg and Denavit describe kinematic synthesis as

...it is design, the creation of something new. Kinematically, it is the conversion of a motion idea into hardware.

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.

References

  1. 1 2 3 Dong, Dianbiao, et al. "Design and optimization of a powered ankle-foot prosthesis using a geared five-bar spring mechanism". International Journal of Advanced Robotic Systems 14.3 (2017): 1729881417704545. p. 3.
  2. 1 2 3 Campion, Gianni. "The Pantograph Mk-II: a haptic instrument." The Synthesis of Three Dimensional Haptic Textures: Geometry, Control, and Psychophysics. Springer, London, 2005. 45-58.
  3. 1 2 Yeh, Xiyang. "2-DOF Pantograph Haptic Device for General Educational Purposes". Collaborative Haptics and Robotics in Medicine Lab at Stanford University. Retrieved 1 June 2020.
  4. He, Dong; Zhihong Sun; and W. J. Zhang. researchgate.net; "A note on inverse kinematics of hybrid actuation robots for path design problems". ASME 2011 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers Digital Collection, 2011.
  5. Khalil, Islam. "Modeling of a Pantograph Haptic Device" (PDF). Medical Micro & Nano Robotics Laboratory (MNRLab), Department of Mechatronics Engineering, German University in Cairo. Retrieved 1 June 2020.
  6. p-themes. "The Best Robot for kids". Wedrawrobot. Retrieved 1 June 2020.
  7. Zhao, Jing-Shan & Liu, Zhi-Jing & Dai, Jian. (2013). "Design of an Ackermann Type Steering Mechanism". Journal of Mechanical Engineering Science. 227. 10.1177/0954406213475980.