Following is the code of PictureBox2, to display the waveform.

Code:
Private Sub PictureBox2_Paint(ByVal sender As Object, ByVal e As System.Windows.Forms.PaintEventArgs) Handles PictureBox2.Paint

        Dim g As Graphics = e.Graphics
        Dim vertFont As New Font("Verdana", 10, FontStyle.Bold)
        Dim horzFont As New Font("Verdana", 10, FontStyle.Bold)
        Dim vertBrush As New SolidBrush(Color.Blue)
        Dim horzBrush As New SolidBrush(Color.Blue)
        Dim horzBrush1 As New SolidBrush(Color.Blue)

        Dim BluePen As New Pen(Color.Blue)

        ' Drawing a vertical and a horizontal line 
        g.DrawLine(BluePen, 50, 225, 50, 15)   'vertical line
        g.DrawLine(BluePen, 50, 120, 260, 120)  'horizontal line


        'Details of the graph layout 
        Dim Origin As New Point(50, 119)
        Dim xAxisLength As Integer = 210
        Dim yAxisLength As Integer = -120

        If voltsQ.Count > 2 Then

            'Turn the queue into an array:
            Dim voltsQarray As Single() = voltsQ.ToArray

            'Define an array of data points:
            Dim DataPoints(voltsQ.Count - 1) As Point
            Dim x, y As Integer

            'Fill in the array using the voltage readings:
            For i As Integer = 0 To voltsQ.Count - 1
                'Get the volts value from the queue:
                Dim v As Single = voltsQarray(i)
                'Find the distance along the x axis:
                x = Origin.X + CInt(i * xAxisLength / 40)
                'find the height of the data point on the Y axis:

                y = Origin.Y + CInt(v * yAxisLength / maxVolts)
                'Put the point in the array
                DataPoints(i) = New Point(x, y)

            Next
            'Draw the waveform:        
            e.Graphics.DrawCurve(Pens.Green, DataPoints)

        End If


        'Draw vertical strings 
        Dim vertStrFormat As New StringFormat()
        vertStrFormat.FormatFlags = StringFormatFlags.DirectionVertical
        g.DrawString("-", horzFont, horzBrush, 49, 113, vertStrFormat)
        g.DrawString("-", horzFont, horzBrush, 49, 113, vertStrFormat)
        g.DrawString("-", horzFont, horzBrush, 59, 113, vertStrFormat)
        g.DrawString("-", horzFont, horzBrush, 69, 113, vertStrFormat)
        g.DrawString("-", horzFont, horzBrush, 79, 113, vertStrFormat)
        g.DrawString("--", horzFont, horzBrush, 89, 106, vertStrFormat)
        g.DrawString("-", horzFont, horzBrush, 99, 113, vertStrFormat)
        g.DrawString("-", horzFont, horzBrush, 109, 113, vertStrFormat)
        g.DrawString("-", horzFont, horzBrush, 119, 113, vertStrFormat)
        g.DrawString("-", horzFont, horzBrush, 129, 113, vertStrFormat)
        g.DrawString("--", horzFont, horzBrush, 139, 106, vertStrFormat)

        g.DrawString("-", horzFont, horzBrush, 149, 113, vertStrFormat)
        g.DrawString("-", horzFont, horzBrush, 159, 113, vertStrFormat)
        g.DrawString("-", horzFont, horzBrush, 169, 113, vertStrFormat)
        g.DrawString("-", horzFont, horzBrush, 179, 113, vertStrFormat)
        g.DrawString("--", horzFont, horzBrush, 189, 106, vertStrFormat)
        g.DrawString("-", horzFont, horzBrush, 199, 113, vertStrFormat)
        g.DrawString("-", horzFont, horzBrush, 209, 113, vertStrFormat)
        g.DrawString("-", horzFont, horzBrush, 219, 113, vertStrFormat)
        g.DrawString("-", horzFont, horzBrush, 229, 113, vertStrFormat)
        g.DrawString("--", horzFont, horzBrush, 239, 106, vertStrFormat)


        ' y-axis drawing 

        g.DrawString("  4 --", vertFont, vertBrush, 25, 12)
        g.DrawString("    --", vertFont, vertBrush, 25, 12)
        g.DrawString("     -", vertFont, vertBrush, 25, 17)
        g.DrawString("     -", vertFont, vertBrush, 25, 22)
        g.DrawString("     -", vertFont, vertBrush, 25, 27)
        g.DrawString("     -", vertFont, vertBrush, 25, 32)

        g.DrawString("  3 --", vertFont, vertBrush, 25, 37)
        g.DrawString("    --", vertFont, vertBrush, 25, 37)
        g.DrawString("     -", vertFont, vertBrush, 25, 42)
        g.DrawString("     -", vertFont, vertBrush, 25, 47)
        g.DrawString("     -", vertFont, vertBrush, 25, 52)
        g.DrawString("     -", vertFont, vertBrush, 25, 57)

        g.DrawString("  2 --", vertFont, vertBrush, 25, 62)
        g.DrawString("    --", vertFont, vertBrush, 25, 62)
        g.DrawString("     -", vertFont, vertBrush, 25, 67)
        g.DrawString("     -", vertFont, vertBrush, 25, 72)
        g.DrawString("     -", vertFont, vertBrush, 25, 77)
        g.DrawString("     -", vertFont, vertBrush, 25, 82)

        g.DrawString("  1 --", vertFont, vertBrush, 25, 87)
        g.DrawString("    --", vertFont, vertBrush, 25, 87)
        g.DrawString("     -", vertFont, vertBrush, 25, 92)
        g.DrawString("     -", vertFont, vertBrush, 25, 97)
        g.DrawString("     -", vertFont, vertBrush, 25, 102)
        g.DrawString("     -", vertFont, vertBrush, 25, 107)
        g.DrawString("  0", vertFont, vertBrush, 25, 112)

        g.DrawString("     -", vertFont, vertBrush, 25, 117)
        g.DrawString("     -", vertFont, vertBrush, 25, 122)
        g.DrawString("     -", vertFont, vertBrush, 25, 127)
        g.DrawString("     -", vertFont, vertBrush, 25, 132)
        g.DrawString("    --", vertFont, vertBrush, 25, 137)
        g.DrawString(" -1--", vertFont, vertBrush, 25, 137)

        g.DrawString("     -", vertFont, vertBrush, 25, 142)
        g.DrawString("     -", vertFont, vertBrush, 25, 147)
        g.DrawString("     -", vertFont, vertBrush, 25, 152)
        g.DrawString("     -", vertFont, vertBrush, 25, 157)
        g.DrawString("    --", vertFont, vertBrush, 25, 162)
        g.DrawString(" -2--", vertFont, vertBrush, 25, 162)

        g.DrawString("     -", vertFont, vertBrush, 25, 167)
        g.DrawString("     -", vertFont, vertBrush, 25, 172)
        g.DrawString("     -", vertFont, vertBrush, 25, 177)
        g.DrawString("     -", vertFont, vertBrush, 25, 182)
        g.DrawString("    --", vertFont, vertBrush, 25, 187)
        g.DrawString(" -3--", vertFont, vertBrush, 25, 187)

        g.DrawString("     -", vertFont, vertBrush, 25, 192)
        g.DrawString("     -", vertFont, vertBrush, 25, 197)
        g.DrawString("     -", vertFont, vertBrush, 25, 202)
        g.DrawString("     -", vertFont, vertBrush, 25, 207)
        g.DrawString("    --", vertFont, vertBrush, 25, 212)
        g.DrawString(" -4--", vertFont, vertBrush, 25, 212)

        ' Dispose of objects 
        vertFont.Dispose()
        horzFont.Dispose()
        vertBrush.Dispose()
        horzBrush.Dispose()
        BluePen.Dispose()

        'Display text in Y-axis
        Dim Font1 As New Font("Comic Sans MS", 10, FontStyle.Bold)
        g.TranslateTransform(30, 148)
        g.RotateTransform(180)
        g.DrawString("Volts (V)", Font1, _
          Brushes.Blue, 0, 0, New StringFormat(StringFormatFlags.DirectionVertical))

    End Sub

Following is the coding for the timer.
I included this line, Single.TryParse(TextBoxVoltage.Text, volts1), so that the waveform will move according to the voltage shown in the "Voltage Level in Volts(V)", and not follow the average voltage(which will produce the straight line).

Code:
 Private Sub Timer3_Tick(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Timer3.Tick

        'read the voltage and get value from RS232 interface
        Call OpenPORT1()

        Single.TryParse(TextBoxVoltage.Text, volts1)
        'add the new reading to the end of the queue
        voltsQ.Enqueue(volts1)

        'remove the old reading at the head of the queue, to keep max. 40 data points    
        If voltsQ.Count > 40 Then voltsQ.Dequeue()

        'update the display with the new data     
        Me.Refresh()

    End Sub
As for Call OpenPORT1(),

Code:
 Private Sub OpenPORT1()
        If SerialPort1.IsOpen Then
            SerialPort1.Close()
        End If

        SerialPort1.PortName = "COM1"
        SerialPort1.BaudRate = 9600
        SerialPort1.Parity = System.IO.Ports.Parity.None
        SerialPort1.DataBits = 8
        SerialPort1.StopBits = System.IO.Ports.StopBits.One

        SerialPort1.RtsEnable = True
        SerialPort1.Open()

    End Sub

I hope everything is correct.