数学代写|ME327 Pantagraphic Analysis
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ME327 Pantagraphic Analysis课程简介
Allison Okamura is indeed a Professor in Mechanical Engineering at Stanford University, with a research focus on haptics and medical robotics. Brandon Ritter and Zonghe Chua were both listed as course assistants for ME 327 during the Spring 2020 semester, and are indeed graduate students in Mechanical Engineering at Stanford University.
PREREQUISITES
Welcome to ME 327: Design and Control of Haptic Systems. The CURRENT offering of this course is in Spring 2022 and course materials for this year should be accessed by Stanford students through Canvas. In contrast, this webpage is offered as a service for the worldwide haptics research and teaching community and includes only course materials from when the class was offered online in Spring 2020. The next offering of ME327 at Stanford will be in Spring 2023. You can also access a lower-level, self-paced MOOC for haptics here: https://hapticsonline.class.stanford.edu/ (free to watch videos, pay for quizzes, assignments, and a certificate). Note that due to changes in availability of parts, the current Hapkit (lab kit) parts list and instructions are out of date. We aim to update these in Summer 2022.
In this class, we study the design and control of haptic systems, which provide touch feedback to human users interacting with virtual environments and teleoperated robots. This class is aimed toward graduate students and advanced undergraduates in engineering and computer science. This class requires a background in dynamic systems and programming. Experience with feedback control and mechanical prototyping is also useful. Course information and policies for 2020 are contained in the syllabus ब. This course covers device modeling (kinematics and dynamics), synthesis and analysis of control systems, design and implementation of mechatronic devices, and human-machine interaction.
ME327 Pantagraphic Analysis HELP（EXAM HELP， ONLINE TUTOR）
Show that equality $|(x \mid y)|=|x||y|$ for the Cauchy-Schwarz inequality holds if and only if $x$ and $y$ are collinear (that is, both belong to some one-dimensional subspace).
Find the transfer function $G_2(s)=Y_h(s) / F_{u p}(s)$, where $y_h(t)$ is the pantograph head displacement.
Give an example of a nonempty compact convex set $C$ in a two-dimensional Banach space $X$ along with a vector $x \in X$ such that the set
$$
\left{c \in C:|x-c|=\min _{y \in C}|x-y|\right}
$$
consists of more than one element.
In this problem we determine some orthogonal complements.
(a) Let
$$
Y:=\left{f \in L^2(0,1): f(t)=0 \text { for almost all } t \in\left(0, \frac{1}{2}\right)\right}
$$
Show that $Y$ is a closed subspace of $L^2(0,1)$ and find $Y^{\perp}$.
(b) Let
$$
Y:=\left{f \in L^2(0,1): \int_0^1 f(t) \mathrm{d} t=0\right} .
$$
Show that $Y$ is a closed subspace of $L^2(0,1)$ and find $Y^{\perp}$.
Textbooks
• An Introduction to Stochastic Modeling, Fourth Edition by Pinsky and Karlin (freely
available through the university library here)
• Essentials of Stochastic Processes, Third Edition by Durrett (freely available through
the university library here)
To reiterate, the textbooks are freely available through the university library. Note that
you must be connected to the university Wi-Fi or VPN to access the ebooks from the library
links. Furthermore, the library links take some time to populate, so do not be alarmed if
the webpage looks bare for a few seconds.
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