Notes in Week 1 - Computer Models

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Published	10/15/2024	In an {{c1::Observational study}}:The System Output is {{c2::Recorded as it occurs}}The Response of the system is {{c3::Not influenced}…
Published	10/15/2024	In {{c1::Experimentation}}:We {{c2::Manipulate the environment}} or  {{c3::the response}}
Published	10/15/2024	In the computation of mathematical equations:Tools like {{c1::Calculus}} and {{c2::Queueing theory}} to obtain {{c3::Closed-Form}} Solu…
Published	10/15/2024	If a {{c1::Closed-Form solution}} is not possible, we must use {{c2::approximation}}
Published	10/15/2024	If {{c1::approximation}} cannot be obatined analytically, {{c2::computation}} must be used
Published	10/15/2024	{{c1::Simulation}} is the process of representing a system with a {{c2::model}} in order to generate {{c3::raw data}}
Published	10/15/2024	The data must be {{c1::statistically processed}} to provide insights about the performance of a system
Published	10/15/2024	The {{c1::model}} is a {{c2::conceptual representation}} of a system which represents the modeler's understanding of a system
Published	10/15/2024	The execution of a computer model results in {{c1::synthetic raw data}}
Published	10/15/2024	{{c1::Measurements}} are collected from a {{c2::physical model of the system}}
Published	10/15/2024	A problem statement should include:A set of questions and {{c1::objectives}}{{c2::A description of the assumptions and metrics}} which is used in maki…
Published	10/15/2024	The {{c1::System and Environment}} of a problem is decided in the {{c2::second}} phase of a simulation study.{{c3::Abstraction}} is a useful…
Published	10/15/2024	As the {{c1::complexity}} of a system under study {{c2::increases}}, {{c3::analytical tools}} may fail to capture {{c4::details of…
Published	10/15/2024	The following are some major advantages of simulation:There is no need to build {{c1:: the physical system}}, so knowledge can be aquired at a mi…
Published	10/15/2024	{{c1::Revolute joints}} are a one-DOF kinematic pair which constrains motion to {{c2::pure rotation along a common axis}} with no {{c3::tran…
Published	10/15/2024	{{c1::Prismatic Joints}} are a one-DOF kinematic pair which constrains the motion of two bodies to {{c2::sliding along a common axis}} witho…
Published	10/15/2024	A {{c1::universal joint}} is a two-DOF joint connecting rigid shafts whose {{c2::axes are inclined to each other}} Commonly used in {{c…
Published	10/15/2024	A {{c1::Spherical/Ball Joint}} has 3 DOF and consists of a bearing stud and socket enclosed in a casing . Widely used in automobiles and controll…
Published	10/15/2024	{{c1::image-occlusion:rect:left=.5298:top=.2864:width=.0467:height=.1138}}{{c2::image-occlusion:rect:left=.8117:top=.2984:width=.0453:height=.0959}}{{…
Published	10/15/2024	{{c1::image-occlusion:rect:left=.0054:top=.8769:width=.2965:height=.1105:oi=1}}{{c2::image-occlusion:rect:left=.3472:top=.8622:width=.2775:height=.125…
Published	10/15/2024	The four prinicipal robot manipulator geometries are:{{c1::Articulated, Revolute, or jointed arm}}{{c2::Polar-Coordinate}}{{c3::Cylindrical}}{{c4::Car…
Published	10/15/2024	The goal in {{c1::Forward Kinematics}} is to determine the {{c2::orientation and position}} of the end effector or tool in terms of the&nbsp…
Published	10/15/2024	Laser cutters and most FDM 3D printers are common example of {{c1::Cartesian Robots (PPP Robots)}}
Published	10/15/2024	The {{c1::orientation}} of a tool frame relative to the base frame is a {{c2::dot product}} of two vectors
Published	10/15/2024	The main limitations of Simulation are:The outcome is an {{c1::estimate subject to statstical error}}Simulation can become {{c2::Costly and …
Published	10/15/2024	The {{c1::First}} Phase of a simulation study is the {{c2::Problem}} Phase,Which involves creating a {{c3::detailed description of the …
Published	10/15/2024	The {{c1::second}} phase of a simulation study is the {{c2::system and environment}} phase. The outcome of this should be a {{c3::…
Published	10/15/2024	The {{c1::third}} phase of a simulation study is about devoloping a {{c2::computational model}} of the system.Using {{c3::elementary co…
Published	10/15/2024	The {{c1::fourth}} phase in a simulation study is to {{c2::translate your existing model into code}}
Published	10/15/2024	The {{c1::fifth}} phase of a simulation study is to {{c2::statistically analyse the raw data}}. You want to have a set of statistics that su…
Published	10/15/2024	The {{c1::sixth/final}} phase of a simulation study is to create {{c2::a report}}, which must include all of the {{c3::answers for ques…
Published	10/15/2024	{{c1::Grübler's formula}} calculates the degrees of freedom (DOF) of a mechanism based on the number of links and joints.
Published	10/15/2024	In {{c4::Grübler’s formula}}, \({DOF =}\) {{c1::\(= m \cdot( N - 1 - J) + \sum_{i=1}^{J} f_i \),}} where \( N \) is the {{c2::number of links}} a…
Published	10/15/2024	In Grübler's formula, \( m \) represents the number of degrees of freedom for a {{c1::rigid body}}, with {{c4::\( m = 3 \)}} for {{c3::planar}} and {{…
Published	10/15/2024	In Grübler’s formula, \( f_i \) is the number of {{c1::freedoms provided by joint \( i \)}} and \( c_i \) is the number of constraints, where \( f_i +…
Published	10/15/2024	The term \( m \cdot N - 1 \) in Grübler's formula accounts for the degrees of freedom of all links, including the {{c1::ground link}}.
Published	10/15/2024	If joint constraints are not {{c2::independent}}, Grübler's formula gives a {{c1::lower bound}} for the degrees of freedom.
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