' The parametric function X(t).
Private Function X(ByVal t As Single) As Single
    X = (2000 * (27 * Cos(t) + 15 * Cos(t * 20 / 7)) / 42) _
        / 20
End Function

' The parametric function Y(t).
Private Function Y(ByVal t As Single) As Single
    Y = (2000 * (27 * Sin(t) + 15 * Sin(t * 20 / 7)) / 42) _
        / 20
End Function

Note that DrawCurve places the points it will draw in an array and then uses the DrawLines method once. This is faster than calling DrawLine multiple times.

' Redraw the curve.
Private Sub Form1_Paint(ByVal sender As Object, ByVal e As _
    System.Windows.Forms.PaintEventArgs) Handles _
    MyBase.Paint
    DrawCurve(e.Graphics, _
        Me.Width \ 2, Me.Height \ 2, _
        0, 14 * PI, 0.1)
End Sub

' Draw the curve on the indicated Graphics object.
Private Sub DrawCurve(ByVal gr As Graphics, ByVal cx As _
    Integer, ByVal cy As Integer, ByVal start_t As Single, _
    ByVal stop_t As Single, ByVal dt As Single)
    Dim num_pts As Integer
    Dim pts() As PointF
    Dim pt As Integer
    Dim t As Single
    Dim px As Single
    Dim py As Single

    ' Allocate room for the points.
    ' Note that this allocates an array 
    ' with indices from 0 to num_pts.
    num_pts = (stop_t - start_t) / dt
    ReDim pts(num_pts)

    ' Find the center of the drawing area.
    px = cx + X(start_t)
    py = cy + Y(start_t)

    ' Find the points.
    t = start_t
    For pt = 0 To num_pts - 1
        pts(pt).X = cx + X(t)
        pts(pt).Y = cy + Y(t)
        t += dt
    Next pt

    ' Close to the first point.
    pts(num_pts) = pts(0)

    ' Draw the lines.
    gr.DrawLines(New Pen(Color.Black), pts)
End Sub

See my book Visual Basic Graphics Programming for more information on drawing cycloids and other curves normally or transformed (stretched, squashed, or rotated). This book uses VB 5/6 not VB .NET.