custom spacing for chapter page, and page number for normal page

Question

I am trying to get the following geometry. I have geometry set like this: \usepackage[a4paper, top=4cm,bottom=2.5cm,right=2.5cm,left=4cm, headheight=15pt]{geometry} and I am using the book document class. I have been looking for some ideas on how to set a specific number of lines before and after the chapter's name (see figure 1), but without success. I am also required to have the page number 1.5cm above the first line of the text (see figure 2), but I do not know how to control it. Chapter page does not require page number, but others page do. Any help will be very much appreciated.

Figure1:

FIgure2:

EDIT: Some more details, all I have been specified is to have a 4cm top and left margin, and a 2.5cm bottom and right margin. That is why I used the geometry package as indicated above. The pagenumber has to be at the top right of the page. Also, I am using a 12pt font size and Times New Roman and XeLatex. For the chapter name I am using the \large size.

Answer 1

Here is what I understood of your requirements:

\documentclass[12pt, a4paper, oneside]{book}%
\usepackage[top=4cm,bottom=2.5cm,right=2.5cm,left=4cm, headheight=15pt, showframe]{geometry}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{fourier}
\usepackage{lipsum,setspace }
\usepackage[pagestyles, clearempty]{titlesec}

\newpagestyle{myps}{%
\assignpagestyle{\chapter}{empty}
\sethead[\thepage][][]{}{}{\thepage}
\setfoot{}{}{}}%

\titleformat{\chapter}[display]{\Large\bfseries}{\chaptername~\thechapter}{0pt}{}
\titlespacing*{\chapter}{0pt}{32pt}{28pt}%
\titlespacing*{name=\chapter, numberless}{0pt}{54pt}{28pt}%
\pagestyle{myps}

\begin{document}

\chapter{A first chapter}

\lipsum[1-6]

\chapter*{Test chapter}

\lipsum[2-3]

\end{document}