反恐防暴知识Modeling Degrees of Freedom
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About Joints
Modeling Joints
Creating a Joint
Modeling Massless Connectors
Modeling Disasmbled Joints
About Joints
A SimMechanics joint reprents the degrees of freedom (DoF) that one body (the follower) has relative to another body (the ba). The ba body can be a movable rigid body or a ground. Unlike a physical joint, a SimMechanics joint has no mass, although some joints have spatial extension (e the Modeling Massless Connectors ction).
A SimMechanics joint does not necessarily imply a physical connection between two bodies. For example, a SimMechanics Six-DoF joint allows the follower, e.g., an airplane, unconstrained movement relative to the ba, e.g., ground, and does not require that the follower ever come into contact with the ba.
SimMechanics joints only add degrees of freedom to a machine, becau the Body blocks carry no degrees of freedom. Contrast this with physical joints, which both add DoFs (with axes of motion) and remove DoFs (by connecting bodies). See Counting Model Degrees of Freedom in this chapter for more on this point.
The SimMechanics Joints Library provides an extensive lection of blocks for modeling various types of joints. This ction explains how to u the blocks.
Note A SimMechanics joint reprents the relative degrees of freedom of one body relative to another body. Only if a joint is connected on one side to a ground and on the other to a body does the joint reprent an absolute DoF of the body with respect to World.
Modeling Joints
Modeling with Joint blocks requires an understanding of the following key concepts:
Joint primitives
Joint types
Joint axes
Joint directionality
Asmbly restrictions
Joint Primitives
Each Joint block bundles together one or more joint primitives that together specify the degrees of freedom that a follower body has relative to the ba body. The following table summarizes the joint primitives found singly or multiply in Joint blocks.
Joint Types
The blocks in the SimMechanics Joint Library fall into the following categories:
Primitive joints
Each of the blocks contains a single joint primitive. For example, the Revolute block contains a revolute joint primitive.
Composite joints
The blocks contain combinations of joint primitives, enabling you to specify multiple rotational and translational degrees of freedom of one body relative to another. Some model idealized real joints, for example, the Gimbal and Bearing joints.
Others specify abstract combinations of degrees of freedom. For example, the Six-DoF block specifi
es unlimited motion of the follower relative to the ba.
The Custom Joint allows you to create joints with any desired combination of rotational and translational degrees of freedom, in any order. The prefabricated composite Joints of the Joints library have the type and order of their primitives fixed. See Axis Order following.
Massless connectors
The blocks reprent extended joints with spatially parated joint primitive axes, for example, a Revolute-Revolute Massless Connector.
Disasmbled joints
奠基典礼The blocks reprent joints not asmbled until simulation starts —for example, a Disasmbled Prismatic.
See the Asmbly Restrictions and Modeling Disasmbled Joints ctions.
Joint Axes
Joint blocks define one or more axes of translation or rotation along which or around which a follower block can move in relation to the ba block. The axes of a Joint block are the axes defined by its component primitives:
A prismatic primitive defines an axis of translation.
A revolute primitive defines an axis of revolution.
A spherical primitive defines a pivot point for axis-angle rotation.
For example, a Planar Joint block combines two prismatic axes and hence defines two axes of translation.
Axis Direction. By default the axes of prismatic and revolute primitives point in the same direction as the z-axis of the World coordinate system (CS). A Joint block's dialog box allows you to point its prismatic and revolute axes in any other direction (e Directing Joint Axes).
Axis Order. Composite SimMechanics Joints execute their motion one joint primitive at a time. A joint that defines more than one axis of motion also defines the order in which the follower body moves along each axis or about a pivot. The order in which the axes and/or pivot appear in the Joint block's dialog box is the order in which the follower body moves.
Different primitive execution orders are physically equivalent, unless the joint includes one spherical or three revolute primitives. Pure translations and pure two-dimensional rotations are independent of primitive ordering.
Axis Span. The span of the primitive axes is the complete space spanned by their combination. For example, one primitive axis defines a line, and two primitive axes define a plane.
Joint Directionality
Directionality is a property of a joint that determines the dependence of the joint on the sign of forces or torques applied to it. A joint's directionality also determines the sign of signals output by nsors attached to the joint. Every SimMechanics joint in your model has a directionality. You must be able to determine the directionality of a joint in order to actuate it correctly and to interpret the output of nsors attached to it.续母
医院投诉管理办法A joint's follower moves relative to the joint's ba. The joint's directionality takes into account the joint type and the direction of the joint's axis, as follows.
Directionality of a Prismatic Joint. If the joint is prismatic, a positive force applied to the joint moves the follower in the positive direction along the axis of translation. A nsor attached to the joint outputs a positive signal if the follower moves in a positive direction along the joint's axis of translation relative to the ba.
Directionality of a Revolute Joint. If the joint is revolute, a positive torque applied to the joint rotates the follower by a positive angle around the joint's axis of rotation, as determined by the right-hand rule. A nsor attached to the revolute joint outputs a positive signal if the follower rotates by a positive angle around the joint's axis of revolution, as determined by the right-hand rule.
Directionality of a Spherical Joint. Spherical joint directionality means the positive n of rotation of the three rotational DoFs. Pick a rotation axis, rotating using the right-hand rule from the ba Body CS axes. Then rotate the
follower Body about that axis in the right-handed n.
Directionality and Ordering of Composite Joint Primitives. Each joint primitive parately has its own directionality, bad on the primitive's type and the direction of its axis of translation or rotation. In ea
ch ca, the follower body of the composite joint moves along or around the joint primitive's axis relative to the ba body.
The order of primitives in the composite Joint's dialog determines the spatial construction of the joint.
The first listed primitive is attached to the ba, the cond to the first, and so on, down to the follower, which is attached to the last primitive.
Moving the first listed primitive moves the subquent primitives in the list, including the follower, relative to the ba.
Moving any primitive moves the primitives below it in the list (but not tho above it), as well as the follower.
Moving the last listed primitive moves only the follower.
Changing the Directionality of a Joint. You can change the directionality of a joint by either
Reversing and reconnecting the Joint block to rever the roles of the ba and follower bodies.
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去黑头收缩毛孔Reversing the sign (direction) of the joint axis.
Asmbly Restrictions
Many joints impo one or more restrictions, called asmbly restrictions, on the placement of the bodies that they join. The
conjoined bodies must satisfy the restrictions at the beginning of simulation and thereafter within asmbly tolerances
that you can specify (e Controlling Machine Asmbly in the Running Mechanical Models chapter). For example, the Body CSs attached to revolute and spherical joints must coincide within asmbly tolerances; the Body CSs attached to a Prismatic joint must lie on the prismatic axis within asmbly tolerances; the Body CSs attached to a Planar joint must be coplanar with Planar primitives, etc. Composite joints, e.g., the Six-DoF joint, impo asmbly restrictions equal to the most restrictive of its joint primitives. See the block reference for each Joint for information on the asmbly restrictions, if any, that it impos.
Positioning bodies so that they satisfy a joint's asmbly restrictions is called asmbling the joint.
All SimMechanics Joints except blocks in the Disasmbled Joints sublibrary require manual asm
bly. Manual asmbly entails your tting the initial positions of conjoined bodies to valid locations (e Asmbling Joints). The simulation asmbles disasmbled joints during the model initialization pha. It assumes that you have already asmbled all other joints before the start of simulation. Hence joints that require manual asmbly are called asmbled joints. During model initialization and at each time step, the simulation also checks to ensure that your model's bodies satisfy all asmbly restrictions. If any of your model bodies fails to satisfy asmbly restrictions, the simulation stops and displays an error message.
Creating a Joint
A joint must connect exactly two bodies. To create a joint between two bodies:
1.Select the Joint from the SimMechanics Joints library that best reprents the degrees of freedom of the follower
body relative to the ba body.
2.Connect the ba connector port of the Joint block (labeled B) to the Body CS origin on the ba block that rves
as the point of reference for specifying the degrees of freedom of the follower block.
3.Connect the follower connector port of the Joint block (labeled F) to the Body CS origin on the follower block that
rves as the point of reference for specifying the degrees of freedom of the ba block.
4.Specify the directions of the joint's axes (e Directing Joint Axes).
5.If you plan to attach Sensors or Actuators to the Joint, create an additional port for each Sensor and Actuator (e
Creating Actuator and Sensor Ports on a Joint).
6.If the joint is an asmbled joint, asmble the bodies joined by the joint (e Asmbling Joints).
Directing Joint Axes
By default the prismatic and revolute axes of a joint point in the same direction as the z-axis of the World coordinate system. To change the direction of the axis of a joint primitive:
1.Open the joint's dialog box and lect a reference coordinate system for specifying the axis direction from the
coordinate system list associated with the axis primitive.
The options are the World coordinate system or the local coordinate systems of the ba or follower attachment point. Choo the coordinate system that is most convenient.
2.Enter in the primitive's axis direction field a vector that points in the desired direction of the axis in the lected
coordinate system.
Creating Actuator and Sensor Ports on a Joint
To create additional connector ports on a Joint for Actuators and Sensors, open the Joint's dialog box and t the Number of nsor/actuator ports to the number of Actuators and Sensors you plan to attach to the Joint.
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Apply the tting by clicking OK or Apply.
Asmbling Joints
You must manually asmble all asmbled joints in your model. Asmbling a joint requires tting the initial positions of its attached ba and follower Body CSs such that they satisfy the asmbly restrictions impod by the joint (e Asmbly Restrictions). Consider, for example, the Modeling and Simulating a Clod-Loop Machine in the Modeling, Simulating, and Visualizing Simple Machines chapter.
This model compris three bars connected by revolute joints to each other and to two ground points. The model collocates the CS origins of the Body CS ports connected to each Joint, thereby satisfying the asmbly restrictions impod by the revolute joints.
Asmbled Revolute Joint in the Four Bar Mechanism
Modeling Massless Connectors
Massless connectors simplify the modeling of machines that u a relatively light body to connect two relatively massive bodies. For example, you could u a Body block to model such a connector.
突如其来造句But the resulting equations of motion might be ill-conditioned, becau that connecting body's mass is small, and the simulation can be slow or prone to failure. A massless connector also avoids global inconsistencies that can ari if you u a Constraint block to model the connector.
A massless connector consists of a pair of joints located a fixed distance apart. Think of a massless connector as a massless rod with a joint primitive affixed at each end.
