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ME451 Kinematics and Dynamics of Machine
Systems
ME451的運動學和機械系統動力學
授課老師: 謝銘源
組員: 黃靖凱 莊沛語
Why/How do bodies move?
Why?
The configuration of a mechanism changes in time based on forces and motions
applied to its components
Forces
Internal (reaction forces)
External, or applied forces (gravity, compliant forces, etc.)
Motions
Somebody prescribes the motion of a component of the mechanical
system
Recall Finite Element Analysis, boundary conditions are of two types:
Neumann, when the force is prescribed
Dirichlet, when the displacement is prescribed
How?
They move in a way that obeys Newton’s second law
Caveat: there are additional conditions (constraints) that need to be satisfies
by the time evolution of these bodies, and these constraints come from the
joints that connect the bodies (to be covered in detail later…)
Putting it all together…
MECHANICAL SYSTEM = BODIES + JOINTS + FORCES
THE SYSTEM CHANGES ITS CONFIGURATION IN TIME
WE WANT TO BE ABLE TO PREDICT & CHANGE/CONTROL HOW SYSTEM
EVOLVES
Examples of Mechanisms
當我說“機械系統”或“系統”這是什麼意思？
What do I mean when I say “mechanical system”, or “system”?
切割行程
雨刮器
工作部件
搖桿耦合
齒輪
左蹺板
曲軸
右蹺板
曲軸耦合器
雨刷機構
Windshield wiper mechanism
快速返回插齒機構
Quick-return shaper mechanism
固定齒輪
路徑
行程運動
轉動曲柄
連接
鋸齒齒輪
雨刷連動方式
機構
More examples …
球形接頭
活塞杆
平移關節
支撐主軸裝配
降低控制
McPherson Strut Front Suspension
麥弗遜式支柱前懸掛
Schematic of car suspension
汽車懸架示意圖
麥弗遜式懸掛系統的優點是：
結構簡單 ，懸掛重量輕和占用空
間小，車輪跳動時前輪定位參數
變化小，有良好的操縱穩定性。
懸挂係統的組成
一、彈簧
二、避震器
三、防傾桿
四、連桿
懸掛係統汽車，車架與車橋或
車輪之間的一切傳力連接裝置的總
稱，其功能是傳遞作用在車輪和車
架之間的力和力矩，並且緩衝由不
平路面傳給車架或車身的衝擊力，
並衰減引起的震動，以保證汽車平
順行駛。懸挂係統應有的功能是支
持車身，改善乘坐的感覺，不同的
懸挂設置會使駕駛者有不同的駕駛
感受。外表看似簡單的懸挂係統綜
合多種作用力，決定著轎車的穩定
性、舒適性和安全性，十分關鍵之
一。
More examples …
Interest here is in controlling the time evolution of these
mechanical systems
機器人機械手
Robotic Manipulator
發動機的截面
Cross Section of Engine
Nomenclature(命名法)
Mechanical System, definition:
A collection of interconnected rigid bodies that can move relative
to one another, consistent with joints that limit relative motions
of pairs of bodies
Why type of analysis can one speak of in conjunction with
a mechanical system?
Kinematics analysis (運動學分析)
Dynamics analysis (動力學分析)
Inverse Dynamics analysis (反向動力學分析)
Equilibrium analysis (均衡分析)
Kinematics Analysis (運動學分析)
Concerns the motion of the
system independent of the
forces that produce the motion
Typically, the time history of one
body in the system is
prescribed
We are interested in how the rest
of the bodies in the system
move
Requires the solution linear and
nonlinear systems of equations
雨刷機械
Dynamics Analysis (動力學分析)
Concerns the motion of the system that
is due to the action of applied
forces/torques
Typically, a set of forces acting on the
system is provided. Motions can
also be specified on some bodies
We are interested in how each body in
the mechanism moves
Requires the solution of a combined
system of differential and algebraic
equations (DAEs)
Inverse Dynamics Analysis(反向動力
學分析)
It is a hybrid between Kinematics and Dynamics
Basically, one wants to find the set of forces that lead to a certain
desirable motion of the mechanism
Your bread and butter in Controls…
這是一個運動學和動力學之間的混合
Windshield wiper mechanism
機器人機械手
Robotic Manipulator
End: Chapter 1 (Introduction)
Begin: Review of Linear Algebra
結束：第1章（引言）開始審查線
性代數
Why bother with vectors/matrices?
Kinematics (and later Dynamics), is all about being able to say at a
given time where a point is in space, and how it is moving.
Vectors and matrices are extensively used to this end.
Vectors are used to locate points on a body.
Matrices are used to describe the orientation of a body.
Geometric Vectors
What is a Geometric Vector?
A quantity that has two attributes:
A direction
A magnitude
VERY IMPORTANT:
Geometric vectors are quantities that exist independently of any
reference frame
ME451 deals almost entirely with planar kinematics and dynamics
We assume that all the vectors are defined in the 2D plane
Geometric Vectors: Operations
What can you do with geometric vectors?
Scale them
Add them (according to the parallelogram rule)
Addition is commutative
– Multiply two of them
• Inner product (leads to a number)
• Outer product (leads to a vector, perpendicular on the plane)
– Measure the angle  between two of them
單位坐標向量（短途旅行）
Unit Coordinate Vectors(short excursion)
單位坐標向量：一個用來表達所有其他向量的單位向量
在這個類中，以簡化我們的生活中，我們使用兩個正交的單位向量
一個向量分解為組件
命名 :
和
和
沿X和Y軸
被稱為笛卡爾向量的組件
符號約定：在本類中，向量/矩陣粗體，標量不（通常是他們以斜體）
幾何向量:操作
Geometric Vectors: Operations
兩個向量的積
關於兩個向量之間的的角度，請注意
兩個向量的點積是可交換

由於坐標單位矢量之間的角度是 / 2：