kinematics In physics, kinematics studies the geometrical aspects of motion of physical objects independent of forces that set them in motion. Constrained motion such as linked machine parts are also described as kinematics. Kinematics is concerned with s ...

, a five-bar linkage is a

mechanism Mechanism may refer to: *Mechanism (economics), a set of rules for a game designed to achieve a certain outcome **Mechanism design, the study of such mechanisms *Mechanism (engineering), rigid bodies connected by joints in order to accomplish a ...

with two

degrees of freedom In many scientific fields, the degrees of freedom of a system is the number of parameters of the system that may vary independently. For example, a point in the plane has two degrees of freedom for translation: its two coordinates; a non-infinite ...

that is constructed from five links that are connected together in a closed chain. All links are connected to each other by five

joints A joint or articulation (or articular surface) is the connection made between bones, ossicles, or other hard structures in the body which link an animal's skeletal system into a functional whole.Saladin, Ken. Anatomy & Physiology. 7th ed. McGraw- ...

in series forming a loop. One of the links is the ground or base.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. This configuration is also called a pantograph,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. however, it is not to be confused with the

parallelogram In Euclidean geometry, a parallelogram is a simple polygon, simple (non-list of self-intersecting polygons, self-intersecting) quadrilateral with two pairs of Parallel (geometry), parallel sides. The opposite or facing sides of a parallelogram a ...

-copying linkage

pantograph A pantograph (, from their original use for copying writing) is a Linkage (mechanical), mechanical linkage connected in a manner based on parallelograms so that the movement of one pen, in tracing an image, produces identical movements in a se ...

. The linkage can be a one-degree-of-freedom mechanism if two

gear A gear or gearwheel is a rotating machine part typically used to transmit rotational motion and/or torque by means of a series of teeth that engage with compatible teeth of another gear or other part. The teeth can be integral saliences or ...

s are attached to two links and are meshed together, forming a geared five-bar mechanism. Five-bar linkage animation

Robotic configuration

When controlled motors actuate the linkage, the whole system (a mechanism and its actuators) becomes a robot. This is usually done by placing two

servomotor A servomotor (or servo motor or simply servo) is a rotary or linear actuator that allows for precise control of angular or linear position, velocity, and acceleration in a mechanical system. It constitutes part of a servomechanism, and consi ...

s (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 An end effector is the device at the end of a robotic arm, designed to interact with the environment. The exact nature of this device depends on the application of the robot. In the strict definition, which originates from serial robotic manipu ...

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 In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all ...

. This robotic configuration is a

parallel manipulator 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 mo ...

. It is a parallel configuration robot as it is composed of two controlled

serial manipulator 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 havin ...

s 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 The moment of inertia, otherwise known as the mass moment of inertia, angular/rotational mass, second moment of mass, or most accurately, rotational inertia, of a rigid body is defined relatively to a rotational axis. It is the ratio between ...

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

Kinematics and dynamics

Both the

forward Forward is a relative direction, the opposite of backward. Forward may also refer to: People *Forward (surname) Sports * Forward (association football) * Forward (basketball), including: ** Point forward ** Power forward (basketball) ** Smal ...

and

inverse kinematics 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 g ...

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. Dynamic modeling of this robotic configuration has been done by Khalil and Abu Seif, forming an

equations of motion In physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time. More specifically, the equations of motion describe the behavior of a physical system as a set of mathem ...

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. It has also been used in the automatic drawing toy WeDraw. A novel Ackermann-type steering mechanism design by Zhao et al. utilized a five-bar linkage instead of the regular four-bar linkage.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. A

prosthetic In medicine, a prosthesis (: prostheses; from ), or a prosthetic implant, is an artificial device that replaces a missing body part, which may be lost through physical trauma, disease, or a condition present at birth (Congenital, congenital disord ...

ankle-foot by Dong et al. used a geared five-bar spring mechanism to simulate the stiffness and damping behavior of a real foot.

References

{{reflist Robot kinematics Robotics engineering