### 数学代写|matlab仿真代写simulation代做|Kinematic Pairs

MATLAB是一个编程和数值计算平台，被数百万工程师和科学家用来分析数据、开发算法和创建模型。

MATLAB主要用于数值运算，但利用为数众多的附加工具箱，它也适合不同领域的应用，例如控制系统设计与分析、影像处理、深度学习、信号处理与通讯、金融建模和分析等。另外还有配套软件包提供可视化开发环境，常用于系统模拟、动态嵌入式系统开发等方面。

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• Foundations of Data Science 数据科学基础

## 数学代写|matlab仿真代写simulation代做|Kinematic Pairs

Linkages are made up of links and joints and are basic elements of mechanisms and robots. A link (element or member) is a rigid body with nodes. The nodes are points at which links can be connected. Figure $1.1$ shows a link with two nodes, a binary link. The links with three nodes are ternary links. A kinematic pair or a joint is the connection between two or more links. The kinematic pairs give relative motion between the joined elements. The degree of freedom of the kinematic pair is the number of independent coordinates that establishes the relative position of the joined links.

A joint has $(6-i)$ degrees of freedom where $i$ is the number of restricted relative movements. A planar one degree of freedom kinematic pair, $c_{5}$, removes 5 degrees of freedom and allows one degree of freedom. The planar two degrees of freedom kinematic pair, $c_{4}$, has two degrees of freedom and removes 4 degrees of freedom. To find the degrees of freedom of a kinematic pair one element is hold to be a reference link and the position of the other element is found with respect to the reference link. Figure 1.2a shows a slider (translational or prismatic) joint that allows one translation (T) degree of freedom between the elements 1 and 2. Figure $1.2 b$ represents a rotating pin (rotational or revolute) joint that allows one rotational (R) degree of freedom between links 1 and 2 . The slider and the pin joints are $c_{5}$ joints. The $c_{5}$ joints allow one degrees of freedom and is called full-joint. For the two degrees of freedom joints, $c_{4}$, there are two independent, relative motions, translation (T) and rotation (R), between the joined links. Two degrees of freedom joints are shown in Fig. 1.3. The two degrees of freedom joint is called half-joint and has 4 degrees of constraint. For a planar system there are two kinds of joints $c_{5}$ and $c_{4}$. A joystick (ball-and-socket joint, or a sphere joint) is a three degrees of freedom joint ( 3 degrees of constraint,$\left.c_{3}\right)$ and allows three independent motions. An example of a four degrees of freedom joint, $c_{2}$, is a cylinder on a plane. A five degrees of freedom joint, $c_{1}$, is represented by a sphere on a plane. The contact between the links can be a point, a curve, or a surface. A point or curve contact defines a higher joint and a surface contact defines a lower joint. The order of a joint is defined as the number of links joined minus one. Two connected links have the order one (one joint) and three connected links have the order two (two joints).

## 数学代写|matlab仿真代写simulation代做|Degrees of Freedom

The number of independent variables that uniquely defines the position of a mechanical system in space at any time is defined as the number of degrees of freedom (DOF). The number of DOF is stated about a reference frame.

Figure $1.4$ represents a rigid body (RB) moving on $x y$-plane. The distance between any two particles on a rigid body is constant at any time. Three DOF are needed to define the position of a free rigid body in planar motion: two linear coordinates $(x, y)$ to define the position of a point on the rigid body, and one angular coordinate $(\theta)$ to define the angle of the body with respect to the reference axes. The particular selection of the independent measurements to define its position is not unique. A free rigid body moving in a three-dimensional (3-D) space has six DOF: three lengths $(x, y, z)$, and three angles $\left(\theta_{x}, \theta_{y}, \theta_{z}\right)$. Next only the two-dimensional motion will be presented. A rigid body in planar motion has pure rotation, if the body possesses one point (center of rotation) that has no motion with respect to a fixed reference frame. The points on the body describe arcs with respect to its center. A rigid body in planar motion has pure translation if all points on the body describe parallel paths. A rigid body in planar motion has complex or general plane motion if it has a simultaneous combination of rotation and translation. The points on the body in general plane motion describe non-parallel paths at an instantaneous center of rotation will change its position.

## 数学代写|matlab仿真代写simulation代做|Kinematic Chains

Bodies linked by joints form a kinematic chain as shown in Fig. 1.5. A contour or loop is a configuration described by a closed polygonal chain consisting of links connected by joints, Fig. 1.5a. The closed kinematic chains have each link and each joint incorporated in at least one loop. The closed loop kinematic chain in Fig. $1.5$ a is defined by the links $0,1,2,3$, and 0 . The open kinematic chain in Fig. 1.5b is defined by the links $0,1,2$, and 3 . A mechanism is a closed kinematic chain. A robot is an open kinematic chain. The mixed kinematic chains are a combination of closed and open kinematic chains. The crank is a link that has a complete revolution about a fixed pivot. Link 1 in Fig. 1.5a is a crank. The rocker is a link with oscillatory rotation and is fixed to the ground. The coupler or connecting rod is a link that has complex motion and is not fixed to the ground. Link 2 in Fig. $1.5 \mathrm{a}$ is a coupler. The ground or the fixed frame is a link that is fixed (non-moving) with respect to the reference frame. The ground is denoted with 0 .

A planar mechanism is shown in Fig. 1.6a. The mechanism has five moving links $1,2,3,4,5$, and a fixed link, the ground 0 . The translation along the $i$ axis is denoted by $\mathrm{T}{i}$, and the rotation about the $i$ axis is denoted by $\mathrm{R}{i}$, where $i=x, y, z$. The motion of each link in the mechanism is analyzed in terms of its translation and rotation about the fixed reference frame $x y z$. The link 0 (ground) has no translations and no rotations. The link 1 has a rotation motion about the $z$ axis, $\mathrm{R}{z}$. The link 2 has a planar motion ( $x y$ is the plane of motion) with a translation along the $x$ axis, $\mathrm{T}{x}$, a translation along the $y$ axis, $\mathrm{T}{y}$, and a rotation about the $z$ axis, $\mathrm{R}{z}$. The link 3 (slider) has a rotation motion about the $z$ axis, $\mathrm{R}{z}$. The link 4 has a planar motion $(x y$ the plane of motion) with a translation along $x, \mathrm{~T}{x}$, a translation along $y, \mathrm{~T}{y}$, and a rotation about $z, \mathrm{R}{z}$. The link 5 has a rotation about the $z$ axis, $\mathrm{R}_{z}$.

A graphical construction for the mechanism connectivity is the contour diagram $[3,18]$. The numbered links are the nodes of the diagram and are represented by

circles, and the joints are represented by lines that connect the nodes. Figure $1.6 \mathrm{~b}$ is the contour diagram of the planar mechanism. The link 1 is connected to ground 0 at $A$ and to link 2 at $B$ with revolute joints. The link 2 is connected to link 3 at $C$ with a slider joint. The link 3 is connected to ground 0 at $C$ with a revolute joint. Next, the link 2 is connected to link 4 at $D$ with a revolute joint. Link 2 is a ternary link because it is connected to three links. Link 4 is connected to link 5 at $D$ with a slider joint. Link 5 is connected to ground 0 at $E$ with a revolute joint. The independent contour is the contour with at least one link that is not included in any other contours of the chain. The number of independent contours, $N$, of a kinematic chain is computed as
$$N=c-n$$
where $c$ is the number of joints, and $n$ is the number of moving links.
For the mechanism shown in Fig. 1.6a the independent contours are $N=c-n=$ $7-5=2$, where $c=7$ is the number of joints and $n=5$ is the number of moving links. Some contours of the mechanisms can be selected as: $0-1-2-3-0,0-1-2-4-5-0$, and 0-3-2-4-5-0. Only two contours are independent contours.

ñ=C−n

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。