19-04-2013, 04:22 PM
Spatial mechanisms
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ABSTRACT
A mechanism in which a body moves through a general spatial movement is called a spatial mechanism. An example is the RSSR linkage, which can be viewed as a four-bar linkage in which the hinged joints of the coupler link are replaced by rod ends, also called spherical joints or ball joints. The rod ends allow the input and output cranks of the RSSR linkage to be misaligned to the point that they lie in different planes, which causes the coupler link to move in a general spatial movement. Robot arms, Stewart platforms, and humanoid robotic systems are also examples of spatial mechanisms.
Select this link for an animation of Bennett's linkage, which is a spatial mechanism constructed from four hinged joints.
In spatial three-degrees-of-freedom (two degrees of translational freedom and one degree of rotational freedom) parallel manipulator is proposed. The parallel manipulator consists of a base plate, a movable platform, and three connecting legs. The inverse and forward kinematics problems are described in closed forms and the velocity equation of the new parallel manipulator is given. Three kinds of singularities are also presented. The workspace for the manipulator is analyzed systematically; in particular, indices to evaluate the mobility (in this paper, mobility means rotational capability) of the moving platform of the manipulator will be defined and discussed in detail. Finally, a topology architecture of the manipulator is introduced. The parallel manipulator has wide application in the fields of industrial robots, simulators, micromanipulators, and parallel machine tools
Introduction to Spatial Mechanisms
Mechanisms
A machine consists of an actuator input, a system of mechanisms that generate the output forces and movement, and an interface to the user. Electric motors, hydraulic and pneumatic actuators provide the input forces and movement. This input is shaped by mechanisms consisting of gears and gear trains, belt and chain drives, cam and follower mechanisms, and linkages as well as friction devices such as brakes and clutches. Structural components consist of the frame, fasteners, bearings, springs, lubricants and seals, as well as a variety of specialized machine elementssuch as splines, pins and keys.[4][5] The user interface ranges from switches and buttons to programmable logic controllers and includes the covers that provide texture, color and styling.
Planar and Spatial Mechanisms
Mechanisms can be divided into planar mechanisms and spatial mechanisms, according to the relative motion of the rigid bodies. In a planar mechanisms, all of the relative motions of the rigid bodies are in one plane or in parallel planes. If there is any relative motion that is not in the same plane or in parallel planes, the mechanism is called the spatial mechanism. In other words, planar mechanisms are essentially two dimensional while spatial mechanisms are three dimensional. This tutorial only covers planar mechanisms.
Spatial mechanisms
A mechanism in which a body moves through a general spatial movement is called a spatial mechanism. An example is the RSSR linkage, which can be viewed as a four-bar linkage in which the hinged joints of the coupler link are replaced by rod ends, also called spherical joints or ball joints. The rod ends allow the input and output cranks of the RSSR linkage to be misaligned to the point that they lie in different planes, which causes the coupler link to move in a general spatial movement. Robot arms, Stewart platforms, and humanoid robotic systems are also examples of spatial mechanisms.
Select this link for an animation of Bennett's linkage, which is a spatial mechanism constructed from four hinged joints.
The group SE(3) is six dimensional, which means the position of a body in space is defined by six parameters. Three of the parameters define the origin of the moving reference frame relative to the fixed frame. Three other parameters define the orientation of the moving frame relative to the fixed frame.
Planar mechanism
The majority of mechanisms synthesized and found in application are planar devices. These mechanisms have motion such that all elements move in one plane or in parallel planes. While planar mechanisms have been broadly applied, they lack the ability to perform many general motion-control tasks. In fact, planar mechanisms, as well as spherical mechanisms, form a subset of spatial mechanisms.
Spatial mechanism
Spatial mechanisms are the most general category of kinematic devices. They offer the greatest capability to accomplish any desired kinematic task. Spatial mechanisms can be composed of any number of links and can include joints with any combination of rotational and translational freed
GENERAL
The path and motion generation synthesis methods which will be explained in this chapter are the first synthesis methods developed by means of the algebra of exponential rotation matrices. The main advantage of these methods is that general dyad equations have been presented for single loop spatial linkages with n links (equations (3.1) and (3.2) ) and very similar equations can be written for multiloop spatial linkages. Besides in these methods the mechanism designer directly deals with link lengths and joint angles which make more sense while in some synthesis methods ,designers work with X ,Y and Z coordinates (ref.18,19,26). Finally using these synthesis methods designers can benefit the advantages of the algebra of exponential rotation matrices.
Mechanism Application
There are a number of reasons for the broad application of planar mechanisms.Well defined analysis and synthesis techniques are readily available and are taught to many mechanical engineers. Additionally, there is a variety of synthesis software available for planar mechanism design, such as LINCAGES, Sphinx, and KINSYN
[Erdman, 1995].
On the other hand, spatial mechanisms have not found wide use and acceptance for several reasons. One, is that spatial mechanism synthesis and analysis is typically not taught to engineers in undergraduate education. Techniques for analysis and synthesis of
spatial mechanisms usually involve extensive vector mathematics and linear algebra techniques. Even for the experienced mechanical designer, it is labor intensive and
difficult to design a spatial mechanism. The visualization of these devices can even be difficult. Finally, no computer package exists that combines rudimentary training, synthesis, and analysis of spatial mechanisms in one program.
Spatial Mechanism Alternatives
Due to the inability of practicing engineers to design spatial mechanisms, many spatial kinematic tasks are either done by a robotic manipulator, a machine with multiple planar actuators, or are simply ignored for automation and are performed by human operators. It should be noted that robotic manipulators provide controlled actuation of all the joints in the system, which results in a large number of degrees of freedom. This flexibility may be not necessary for the given task, in which case the manipulator could be replaced with a single degree-of-freedom spatial mechanism
Applications for Spatial Mechanisms
If spatial mechanisms could be synthesized quickly and easily, there could be many suitable applications for them in addition to the examples described above. Some examples include the aerospace industry, exercise equipment, and the rehabilitation medical field. Engineers in aerospace are constantly trying to find ways to make things compact, light weight, and able to perform a specific spatial function.
Degree of freedom
The number of independent movements that an object can perform in a 3-D space is called the number of degrees of freedom (DOF). The movement of an ideal joint is generally associated with a subgroup of the group of Euclidean displacements. The number of parameters in the subgroup is called the degrees of freedom (DOF) of the joint.